Algebra for College Students (10th Edition)

Chapter 10

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; Express 125 as in the given equation.If , and... more

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; Express 25 as in the given equation.Express ... more

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4 ; Express as in the given equation.If , and ... more

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; Express 16 as and 64 as in the given equation... more

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; Express 25 as in the given equation.The power ... more

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Substitute , , 0, 1 and 2 for in the given ... more

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Substitute , , 0, 1 and 2 for in the given ... more

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Substitute , , 0, 1 and 2 for in the given ... more

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1.889 ; Press the ON button to turn on the ... more

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The product law of exponents states that , where ... more

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The product law of exponents states that where ... more

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The expression is equivalent to where is a ... more

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The expression is equivalent to where is a ... more

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The power rule of exponents states that where is... more

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An exponential function is a mathematical function... more

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An exponential function is a mathematical function... more

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The value of becomes larger as the value of ... more

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Exponential functions are defined as , where , ... more

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Any number (except 0) raised to the power 0 is ... more

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; Express 64 as in the given equation.If and , ... more

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; Express 81 as in the given equation.If and , ... more

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; Express 27 as in the given equation.If and , ... more

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; Express 16 as in the given equation.If and , ... more

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; Express 128 as in the given equation.The power... more

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; Express 256 as in the given equation.The power... more

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; Express 243 as in the given equation.The ... more

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; Express 9 as in the given equation.If and , ... more

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; Express 36 as in the given equation.If and , ... more

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; Express 32 as in the given equation.If and , ... more

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; Express 64 as and 27 as in the given equation... more

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; Express 9 as and 4 as in the given equation.... more

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; Express 16 as and 64 as in the given equation... more

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; Express 4 as and 8 as in the given equation.... more

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; Express 27 as and 9 as in the given equation.... more

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; Express 32 as and 16 as in the given equation... more

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; Express 9 as and 81 as in the given equation.... more

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; Express 8 as and 16 as in the given equation.... more

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; Express 0.1 as a power of 10.If and , then if... more

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; Express 0.0001 as a power of 10.If and , then... more

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; Express 64 as in the given equation.The ... more

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; Express 32 as .The product property of ... more

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; Express 81 as a power of 3.The product property... more

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; Express 4, 8 and 16 as a power of 2. The power ... more

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; Express 4, 8 and 16 as a power of 2.The power ... more

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Substitute the values of as and 2 one by one in ... more

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Substitute the values of as and 2 one by one in ... more

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Substitute the values of as and 4 one by one in ... more

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Substitute the values of as and 4 one by one in ... more

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Substitute the values of as in the given ... more

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Substitute the values of as and 4 one by one in ... more

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Substitute the values of as and 3 one by one in ... more

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Substitute the values of as and 3 one by one in ... more

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Substitute the values of as and 3 one by one in ... more

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Substitute the values of as and 3 one by one in ... more

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Substitute the values of as and 3 one by one in ... more

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Substitute the values of as and 3 one by one in ... more

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Substitute the values of as ,, 0 and 2 separately... more

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Substitute the values of as ,, 0 and 2 separately... more

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Substitute the values of as ,, 0, 1 and 2 ... more

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Substitute the values of as , , 0, 1 and 3 ... more

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Substitute the values of as , , 0, 1 and 2 ... more

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Substitute the values of as , , 0, 1 and 2 ... more

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Substitute the values of as , , 0, 1 and 3 ... more

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Substitute the values of as , , 0, 1 and 2 ... more

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Express 8 as , 64 as .Use the power of a power ... more

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The value of does not exist if the value of is ... more

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Take some arbitrary values of , substitute them in... more

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The orange curve shows the graph of , purple curve... more

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The graph of is located 5 units right to the ... more

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The graph of is located 2 units up to the graph ... more

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The graph of is the reflection across -axis of ... more

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Press the ON button to turn on the calculator.... more

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; The compound interest formula is where is the... more

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, ; The exponential decay formula is , where is ... more

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3311 ; The law of exponential growth is given by ... more

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gm ; The law of exponential growth is given by ... more

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About 35 years ; The formula for accumulated money... more

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If a principal money that has been invested for ... more

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The semiannual compounding formula is given by , ... more

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The continuous compounding formula is given by , ... more

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A translation is a transformation that occurs when... more

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A translation is a transformation that occurs when... more

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When a point is reflected across the -axis, the -... more

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; The investment is done annually. Therefore, the... more

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; The investment is done annually. Therefore, the... more

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; The investment is done semiannually. Therefore... more

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; The investment is done semiannually. Therefore... more

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; The investment is done quarterly. Therefore, ... more

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; The investment is done quarterly. Therefore, ... more

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; The investment is done monthly. Therefore, the ... more

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; The investment is done monthly. Therefore, the ... more

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; The investment is done annually. Therefore, the... more

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; The investment is done semiannually. Therefore... more

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; The investment is done quarterly. Therefore, ... more

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; The investment is done monthly. Therefore, the ... more

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; The rate can be written as i.e., 0.07.... more

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; The rate can be written as i.e., 0.06.... more

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; The rate can be written as i.e., 0.08.... more

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; The rate can be written as i.e., 0.05.... more

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; The rate can be written as i.e., 0.07.... more

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; Substitute 5000 for , 20 for and 0.08 for as... more

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; Substitute 7500 for , 10 for and 0.065 for as... more

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; Substitute 10000 for , 25 for and 0.0425 for ... more

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; Substitute 15000 for , 10 for and 0.0575 for ... more

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; If a principal amount is invested at an annual... more

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. ; If a principal amount is invested at an ... more

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; The effective yield for the investment at ... more

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; The effective yield for the investment at ... more

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compounding monthly ; The effective yield for ... more

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compounding quarterly. ; The effective yield for... more

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625 milligrams ; 442 milligrams  ; The half life ... more

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50 grams;37 grams  ; The half life of a ... more

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354 grams  ; The half life of a radioactive ... more

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2226;3320;7389 ; Substitute 2 for in the given ... more

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8244;22408;100428 ; Substitute 10 for in the ... more

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2000 ; Substitute 6640 for and 4 for in the ... more

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203 grams; 27 grams; 0.5 grams ; Substitute 5 for... more

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Substitute , , , 0, 1, and 2 separately for in ... more

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Substitute , , , 0, 1, and 2 separately for in ... more

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Substitute , , , 0, and 1 separately for in the ... more

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Substitute , , , 0, 1, and 2 separately for in ... more

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Substitute , , , 0, and 1 separately for in the ... more

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Substitute , , 0, 1, 2, and 3 separately for in ... more

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Simple interest over a certain period is the fixed... more

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Effective yield can be defined as a yearly rate of... more

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The formula to calculate the exponential decay of ... more

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Substitute some arbitrary values of such as... more

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Substitute some arbitrary values of such as , , 0... more

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Substitute some arbitrary values of such as , , 0... more

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Substitute some arbitrary values of such as , , 0... more

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Substitute the values 0.2, 0.4, 0.5,1, 2 and 3 for... more

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Yes, the graphs are consistent because the graph ... more

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The graphs of the functions and should be ... more

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The graphs of the functions , , and are the ... more

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The graph of the functions and will be more ... more

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The functions and are inverse functions of each ... more

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The functions and are inverse functions of each ... more

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; Substitute for in the given function and ... more

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; Substitute for in the given function and ... more

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The horizontal line test is a visual way to ... more

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The inverse of a function is denoted by the ... more

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The two functions and are said to be an inverse ... more

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The horizontal line test is a visual way to ... more

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A function is said to be a one-to-one function if ... more

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The two functions and are said to be an inverse ... more

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The two functions and are said to be an inverse ... more

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The two functions are said to be an inverse of ... more

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If be a function, and , be the points in the ... more

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A function which is always increasing or ... more

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The horizontal line test is a visual way to ... more

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The horizontal line test is a visual way to ... more

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The horizontal line test is a visual way to ... more

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The horizontal line test is a visual way to ... more

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The horizontal line test is a visual way to ... more

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The horizontal line test is a visual way to ... more

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A function is said to be a one-to-one if each ... more

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A function is said to be a one-to-one if each ... more

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A function is said to be a one-to-one if each ... more

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A function is said to be a one-to-one if each ... more

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A function is said to be a one-to-one if each ... more

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The absolute value of a real number is defined as... more

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If a function is one one then implies that , ... more

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If a function is one one then implies that , ... more

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Apply the law of composition of two functions to ... more

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Apply the law of composition of two functions to ... more

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Apply the law of composition of two functions to ... more

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Apply the law of composition of two functions to ... more

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Apply the law of composition of two functions to ... more

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Apply the law of composition of two functions to ... more

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Apply the law of composition of two functions to ... more

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Apply the law of composition of two functions to ... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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For a one-to-one function with a domain of and a... more

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Increasing: ;Decreasing: ; Consider a function , ... more

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Increasing: ; Consider a function , with as the ... more

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Decreasing: ; Consider a function , with as the ... more

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Increasing: Decreasing: ; Consider a function , ... more

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Increasing: Decreasing: ; Consider a function , ... more

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Increasing: Decreasing: ; Consider a function , ... more

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Increasing:Decreasing: ; Consider a function , ... more

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Increasing: Decreasing: ; Consider a function , ... more

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Replace by in the given equation, i.e., .... more

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Obtain the inverse of the linear function of the ... more

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Yes. Both the given functions are inverses of each... more

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The numbers 2 and are additive inverses of each ... more

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; Consider the given expression as .The ... more

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; Consider the given expression as .Rewrite as .... more

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; The equivalent exponential equation of the ... more

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; The equivalent exponential equation of the ... more

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2.2618 ; The logarithmic product property states ... more

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4.2288 ; The logarithmic product property states ... more

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0.6826 ; The logarithmic division property states ... more

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0.8632 ; The logarithmic division property states ... more

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0.80245 ; The logarithm power property states that... more

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2.761 ; The logarithm power property states that... more

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; The logarithmic product property states that ... more

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; The logarithmic division property states that ... more

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; The logarithmic product property states that ... more

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The logarithm exponential property states that .... more

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The logarithm property states that and .The given... more

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If is any positive real number, then the unique ... more

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The logarithmic power property states that .Use ... more

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The logarithm product property states that , where... more

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The logarithmic property states that and for ... more

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The logarithm is defined only for positive values.... more

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The logarithm product property states that , where... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponentiatial and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponentiation and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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; The relationship between exponential and ... more

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4 ; The relationship between exponential and ... more

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8 ; The relationship between exponentiation and ... more

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4 ; The relationship between exponential and ... more

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9 ; The relationship between exponentiation and ... more

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3 ; The relationship between exponentiation and ... more

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4 ; The relationship between exponentiation and ... more

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; The relationship between exponentiation and ... more

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; Consider as the value of the given expression.... more

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0 ; Consider as the value of the given expression... more

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1 ; Consider as the value of the given expression... more

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; Consider as the value of the given expression.... more

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; Consider as the value of the given expression.... more

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5 ; Consider as the value of the given expression... more

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14 ; Consider as the value of the given ... more

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; Consider as the value of the given expression.... more

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; Consider as the value of the given expression.... more

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1 ; Consider as the value of the expression .... more

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1 ; Consider as the value of the expression .... more

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0 ; Consider as the value of the given expression... more

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0 ; Consider as the value of the given expression... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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; A logarithmic expression of the form is ... more

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5.1293 ; Rewrite the given expression as .Use the ... more

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0.4855 ; Use the property that to expand the ... more

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6.9657 ; Rewrite the given expression as .Use the ... more

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5.6148 ; Rewrite the given expression as .Use the ... more

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1.4073 ; Rewrite the given expression as .Use the ... more

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0.774 ; Rewrite the given expression as .Use the ... more

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7.4512 ; Rewrite the given expression as .Use the ... more

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5.8074 ; Write 56 as the product of 7 and 8.The ... more

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6.3219 ; Write 80 as the product of 5 and 16.The ... more

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1.9271 ; Write 55 as the product of 5 and 11.The ... more

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; The Logarithm quotient rule states that the ... more

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1.548 ; Write 25 as in the given expression.The ... more

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0.5766 ; Write as in the given expression to ... more

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0.516 ; The logarithm power rule states that the ... more

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2.1531 ; Write 88 as the product of 8 and 11.The ... more

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2.7740 ; Write 320 as the product of 5 and 64.The ... more

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0.3949 ; The logarithm quotient rule states that ... more

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0.7582 ; The logarithm quotient rule states that ... more

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; The logarithm product rule states that the ... more

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; The logarithm product rule states that the ... more

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; The logarithm quotient rule states that the ... more

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; The logarithm quotient rule states that the ... more

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; The logarithm product rule states that the ... more

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; The logarithm product rule states that the ... more

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; The logarithm quotient rule states that the ... more

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; The logarithm product rule states that the ... more

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; Write as to convert radical into rational ... more

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; Write as to convert radical into rational ... more

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; The logarithm product rule states that the ... more

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; Write as to convert radical into rational ... more

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; The logarithm power rule states that the  times... more

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; The logarithm product rule states that the the ... more

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; Simplify the given expression and rearrange the... more

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; Take common from the expressions and .The ... more

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; The logarithm power rule states that the  times... more

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; The logarithm power rule states that the  times... more

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; The Logarithm power rule states that the  times... more

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; Use the logarithmic property .Substitute 2 for... more

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; Use the logarithmic property, to simplify the ... more

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; Use the logarithmic property, to simplify the ... more

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; To add the first two terms use the logarithmic ... more

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; To add the first two terms use the logarithmic ... more

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; To add the first two terms use the logarithmic ... more

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; To add the first two terms use the logarithmic ... more

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; To add the first two terms use the logarithmic ... more

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; Rearrange the given equation it means shift the... more

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1.667 ; To add the first two terms use the ... more

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0.71428 ; To add the first two terms use the ... more

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2.375 ; To subtract the first two terms use the ... more

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38 ; Rearrange the given equation it means shift ... more

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9 ; Rearrange the given equation it means shift ... more

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; To add the first two terms use the logarithmic ... more

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; To subtract the first two terms use the ... more

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; Rearrange the given equation it means shift the... more

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; To add the first two terms use the logarithmic ... more

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; To add the first two terms use the logarithmic ... more

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Consider some values for in which we can easily ... more

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0.8597 ; Use the calculator to determine the value... more

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0.3117 ; Use the calculator to determine the value... more

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1.7179 ; Use the calculator to determine the value... more

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3.50705 ; Use the calculator to determine the ... more

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4.15195 ; Use the calculator to determine the ... more

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; Use the calculator to determine the value. ; more

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; Use the calculator to determine the value. ; more

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; Use the calculator to determine the value. ; more

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; Use the calculator to determine the value. ; more

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; Use the calculator to determine the value. ; more

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79.543 ; The definition of the logarithmic ... more

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3.56205 ; The definition of the logarithmic ... more

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0.04844 ; The definition of the logarithmic ... more

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0.71581 ; The definition of the logarithmic ... more

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0.00642 ; The definition of the logarithmic ... more

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0.00222 ; The definition of the logarithmic ... more

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1.6094 ; Press the ON button to turn on the ... more

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2.8904 ; Press the ON button to turn on the ... more

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3.4843 ; Press the ON button to turn on the ... more

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4.3758 ; Press the ON button to turn on the ... more

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6.0638 ; Press the ON button to turn on the ... more

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5.9184 ; Press the ON button to turn on the ... more

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; Press the ON button to turn on the graphing ... more

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; Press the ON button to turn on the graphing ... more

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; Press the ON button to turn on the graphing ... more

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; Press the ON button to turn on the graphing ... more

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1.6034 ; The definition of the logarithmic ... more

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2.5633 ; The definition of the logarithmic ... more

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3.1346 ; The definition of the logarithmic ... more

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15.830 ; The definition of the logarithmic ... more

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108.56 ; The definition of the logarithmic ... more

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20.613 ; The definition of the logarithmic ... more

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0.48268 ; The definition of the logarithmic ... more

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0.19699 ; The definition of the logarithmic ... more

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0.03599 ; The definition of the logarithmic ... more

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0.09306 ; The definition of the logarithmic ... more

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Substitute 0, 1 , 2 , 3 and 4 for in the given ... more

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Substitute , , 0, 1 and 2 for in the given ... more

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Substitute , 0, 1 and 2 for in the given ... more

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Substitute , 0, 1 and 2 for in the given ... more

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Substitute 1, 2, 4 , 8 and 16 for in to obtain ... more

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Substitute 1, 2, 4 , 8 and 16 for in to obtain ... more

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Substitute 1, 2, 4 , 8 and 16 for in to obtain ... more

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Substitute 1, 2, 4 , 8 and 16 for in to obtain ... more

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Substitute 1, 2, 4 , 8 and 16 for in to obtain ... more

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Substitute 1, 2, 4 , 8 and 16 for in to obtain ... more

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Substitute 1, 2, 4 , 8 and 16 for in to obtain ... more

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1.77 ; Press the ON button on the graphing ... more

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0.36 ; Press the ON button on the graphing ... more

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1.06 ; Press the ON button on the graphing ... more

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0.73 ; Press the ON button on the graphing ... more

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27.47 ; Press the ON button on the graphing ... more

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23.10 ; Press the ON button on the graphing ... more

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7.00 ; Press the ON button on the graphing ... more

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7.93 ; Press the ON button on the graphing ... more

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The given logarithmic value can be written in the ... more

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Use the graphing calculator to obtain the graph of... more

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Use the graphing calculator to obtain the graph of... more

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The other three functions on the same set of axes ... more

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The graph of the function is the graph of which ... more

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1.543 ; Take the natural logarithm on both sides ... more

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3.778 ; Take the natural logarithm on both sides ... more

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1.845 ; Take the natural logarithm on both sides ... more

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25 ; The product rule of logarithm states that the... more

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8 ; The product rule of logarithm states that , ... more

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; The product rule of logarithm states that , ... more

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23.133 years approximately ; The compound interest... more

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12 hours approximately ; Substitute 5000 for , ... more

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2,00,00,000 ; The Richter number is given by , ... more

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4 ; Consider two earthquakes with a Richter number... more

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1.5646 ; Rewrite the number 21 in the given ... more

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; Subtract both sides of the given equation by 2.... more

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The logarithmic function , defined for all ... more

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The expression but . Therefore, does not imply ... more

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The given formula represents the exponential ... more

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The higher the value of , the faster is the ... more

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The Richter number is given by the formula where... more

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The quotient property of logarithms states that ... more

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; The definition of a logarithm states that if ... more

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; The definition of a logarithm states that if ... more

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2.6826 ; Divide the given equation by .The ... more

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5.43 ; Subtract 7 from both sides of the obtained ... more

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3.13 ; Add 6 to both sides of the obtained ... more

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; The definition of a logarithm states that if ... more

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1.81 ; The definition of a logarithm states that ... more

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0.12 ; The definition of a logarithm states that ... more

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1.41 ; Divide both sides of the given equation by ... more

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3.30 ; The definition of natural logarithm states ... more

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4.45 ; The definition of natural logarithm states ... more

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4.57 ; The definition of natural logarithm states ... more

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3.10 ; The definition of natural logarithm states ... more

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1.79 ; Add 1 to both sides of the given equation.... more

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1.82 ; Divide both sides of the obtained equation ... more

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2.51 ; Apply the natural logarithmic function on ... more

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; The quotient property of logarithms states that... more

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; The quotient property of logarithms states that... more

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8 ; Subtract from both sides of the given ... more

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6 ; The quotient property of logarithms states ... more

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; The exponent property of logarithms states that... more

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5.322 ; The change of base formula for logarithms ... more

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6.539 ; The change of base formula for logarithms ... more

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2.524 ; The change of base formula for logarithms ... more

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3.287 ; The change of base formula for logarithms ... more

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0.339 ; The change of base formula for logarithms ... more

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0.839 ; The change of base formula for logarithms ... more

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; Consider the given expression as equal to .... more

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3.194 ; Consider the given expression as equal to... more

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3.184 ; Consider the given expression as equal to... more

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4.8 years ; The formula to calculate the ... more

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11.7 years ; The formula to calculate the ... more

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17.3 years ; The formula for the accumulated value... more

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22 years ; The formula for the accumulated value ... more

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6100 feet ; Substitute 11.53 for in the given ... more

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34.7 years ; Substitute 100000 for and 50000 for... more

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7 ; The formula for the Richter number is , where... more

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200 million ; The formula for the Richter number ... more

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8 times ; The formula for the Richter number is , ... more

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501 times ; The formula for the Richter number is... more

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Consider the given expression as and then change ... more

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Richter number compares the intensity of ... more

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2.1461 ; Use the graphing calculator to obtain the... more

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5.4638 ; Use the graphing calculator to obtain the... more

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3.19 ; The change of base formula states that , ... more

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Substitute for in the given expression.The ... more

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; The product rule for logarithms states that , ... more

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; The quotient rule for natural logarithms states... more

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32 ; The property for the number with rational ... more

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81 ; The property for the number with rational ... more

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3 ; The change of base formula states that where... more

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; The quotient rule for logarithms states that , ... more

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1 ; The base of the logarithm in the given ... more

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12 ; The logarithmic property states that for any... more

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5 ; The product rule for logarithms states that , ... more

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3.40 ; The property of logarithm states the ... more

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20 ; The product rule for common logarithms states... more

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2 ; The quotient rule for common logarithms states... more

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0 ; Express both the terms and in powers of 2.... more

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1.3222 ; Substitute for 21 in the given ... more

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0.5634 ; The power rule for logarithms states that... more

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0.631 ; The change of base formula states that , ... more

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3.789 ; The change of base formula states that , ... more

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; The change of base formula states that , where... more

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Substitute , , 0, 1  and 2 for successively in ... more

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Substitute 3.1, 4, 5, 6 and 7 for successively in... more

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Substitute for in the given equation.Interchange... more

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Substitute for in the given equation.Interchange... more

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Substitute for in the given equation.Interchange... more

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Substitute for in the given equation.Interchange... more

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Increasing ; A function is said to be increasing ... more

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61,070; 64,793; 74,591 ; Substitute 50,000 for ... more

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1 ; The power rule of logarithm states that , ... more

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56 ; Substitute 16 for and and 16 for in the ... more

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72 ; Use the property, , where is a non-zero real... more

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6 ; Equate the given logarithmic expression to to... more

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300 ; Write 0.00072 as and  0.0000024 as The ... more

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