Algebra and Trigonometry (5th Edition)

Chapter 5

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; The first coordinate of the ordered pair ... more

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; The first coordinate of the ordered pair ... more

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; The first coordinate of the ordered pair ... more

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; The first coordinate of the ordered pair ... more

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; The variable becomes the variable and the ... more

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; The variable becomes the variable and the ... more

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; The variable becomes the variable and the ... more

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; The variable becomes the variable and the ... more

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; The variable becomes the variable and the ... more

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; The variable becomes the variable and the ... more

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Substitute different values of to get ... more

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Substitute different values of to get ... more

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The given equation represents a line. Substitute ... more

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The given equation represents a line. Substitute ... more

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Substitute different values of  to get ... more

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Substitute different values of  to get ... more

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Entire Proof Answer: For the given function to be ... more

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Entire Proof Answer: For the given function to be ... more

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Entire Proof Answer: For the given function to be ... more

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Entire Proof Answer: For the given function to be ... more

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Entire Proof Answer: For the given function not to... more

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Entire Proof Answer: For the given function not to... more

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Entire Proof Answer: For the given function not to... more

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For the given function not to be one to one, find ... more

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One-to-one ; Draw horizontal lines passing through... more

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One-to-one ; Draw horizontal lines passing through... more

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Not one-to-one ; Draw horizontal lines passing ... more

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not one-to-one ; Draw horizontal lines passing ... more

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one-to-one ; Draw horizontal lines passing through... more

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One-to-one ; Draw horizontal lines passing through... more

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One-to-one ; Draw horizontal lines passing through... more

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One-to-one ; Substitute different values of into ... more

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One-to-one ; Substitute different values of into ... more

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Not one-to-one ; Substitute different values of ... more

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Not one-to one ; Substitute different values of ... more

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Substitute different values of into the given ... more

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Not one-to-one ; Draw the graph of . ; Draw the ... more

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One-to-one ; Substitute different values of into ... more

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One-to-one ; Substitute different values of to ... more

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Not one-to-one ; Plot the graph of . ; Draw ... more

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Not one-to-one ; Substitute different values of ... more

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Not one-to-one ; Substitute different values of  ... more

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One-to-one ; Substitute different values of  to ... more

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; As the input is multiplied by 3, to find ... more

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; As the input is multiplied by and then 7 is ... more

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; As the input are output are both inverse of ... more

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; As the cube root is taken for input and then 5 ... more

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; As 5 is subtracted from input and then the cube... more

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; As the input are output are both reciprocal of ... more

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Reflect the points labeled on the graph across the... more

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Reflect the points labeled on the graph across the... more

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; Reflect the points , , , and along the line... more

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; Reflect the points , , , and along the line... more

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; Reflect the given graph across the line to get... more

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; Reflect the given graph across the line to get... more

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Entire Proof Answer: Evaluate .  Evaluate .  ; ... more

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Entire Proof Answer: Evaluate .  Evaluate .  ; ... more

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Entire Proof Answer: Evaluate .  Evaluate .  ; ... more

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Entire Proof Answer: Evaluate .  Evaluate .  ; ... more

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Entire Proof Answer: Evaluate .  Evaluate .  ; ... more

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Entire Proof Answer: Evaluate .  Evaluate .  ; ... more

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Domain of : Range of : Domain of : Range of : ; ... more

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Domain of : Range of : Domain of : Range of : ; ... more

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Domain of : Range of : Domain of : Range of : ; ... more

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Domain of : Range of : Domain of : Range of :   ; ... more

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Domain and range of : ; Domain and range of : ; ; ... more

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Domain and range of : ; Domain and range of : ; ; ... more

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Domain of : and range of : ; Domain of : and ... more

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Domain of : and range of : ; Domain of : and ... more

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5; ; Use the definition of the composition of the ... more

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; 1253 ; Use the definition of the composition of ... more

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The restriction for the function is .The inverse ... more

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No ; The function does not pass the horizontal ... more

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; ; ; The examples of such functions include , , ... more

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If , then and if , then can be any real number... more

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; Enter the given expression into the CAS using ... more

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; Enter the given expression into the CAS using ... more

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; Enter the given expression into the CAS using ... more

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; The value of the given expression can be ... more

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Substitute 0 for  into the function to find the -... more

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Substitute different values of into the given ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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Substitute different values of and calculate the ... more

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The graph of the function can be obtained by ... more

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The graph of the function can be obtained by ... more

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The graph of the given exponential function can be... more

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The graph of the given exponential function can be... more

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The graph of the given function is obtained by ... more

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The graph of the given function is obtained by ... more

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The graph of the given function is obtained by ... more

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The graph of the given function can be obtained by... more

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The graph of the given function can be obtained by... more

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The graph of the given function can be obtained by... more

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 The graph of the given function can be obtained ... more

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The graph of  is shifted by two units to right and... more

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The graph of  is shifted 1 unit rightward. The ... more

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The graph of  is shifted by 1 unit to the left. ... more

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Shrink the graph of the function  horizontally. ; ... more

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The given function's graph can be obtained by ... more

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The given function's graph is obtained by ... more

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The given function's graph is obtained by shifting... more

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The given function's graph is obtained by shifting... more

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The given function's graph is obtained by ... more

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Reflect the graph of  across the -axis, then ... more

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Stretch the graph of horizontally and reflect the... more

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Substitute  for and calculate the corresponding ... more

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Substitute  and  for and calculate the ... more

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; The interest is compounded quarterly; so the ... more

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; The interest is compounded semiannually; so the... more

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; The interest is compounded quarterly; so the ... more

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; As the interest is compounded annually, so .The... more

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; As the interest is compounded quarterly, so .... more

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; As the interest is compounded quarterly, so .... more

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; As the interest is compounded semi-annually, so... more

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; As the interest is compounded daily, so .The ... more

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; As the interest is compounded daily, so .The ... more

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1998: 322,4202010: 938,2972018: 1,912,580 ; ... more

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MP: iM: ; Determine the value of for the year ... more

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2011: million2015: million ; Determine the value... more

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2009: 16,4352011: 41,2922016: 413,194 ; Determine ... more

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2005: 3 million2009: 17 million2012: 54 million ; ... more

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1990: billion2000: billion2012: billion ; ... more

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2020: 101,2342050: 414,387 ; Determine the value ... more

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1985: 495,0002000: 707,0002014: 985,0002020: 1,136... more

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1982: billion1995: billion2010: billion ; ... more

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2010: 32 million2018: 57 million  ; Determine the ... more

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; Substitute 0 for into the given exponential ... more

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; Substitute 0 for into the given exponential ... more

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; Substitute 25 for into the given exponential ... more

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; ; ; ; ; Substitute 1 for into the given ... more

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; Multiple each term of first binomial with every... more

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; Multiply the numerator and the denominator by ... more

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Zeroes: ; 7-intercept: , ; Equate the given ... more

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Zero: 1-intercept: ; The degree of  is 3 which ... more

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Zero: ; 0; 1-intercept: ; ; ; Factor out the ... more

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Zeros: ; 0; 3-intercept: ; ; ; Factor out the ... more

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; 0; 2 ; Equate the given function to 0 and factor... more

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

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; ; The values of , ,  and  are , ,  and  ... more

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; Substitute  for  into  to evaluate . ; ... more

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 Substitute 0 for into the function to find the ... more

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Substitute different values of into the ... more

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Substitute different values of into the ... more

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Substitute different values of into the ... more

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Substitute different values of into the ... more

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Rewrite the given equation such that where is ... more

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Rewrite the given equation such that , where  is ... more

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Rewrite the given equation such that , where  is ... more

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Replace  with  in the expression of the function.... more

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4 ; Express 16 as an exponent of the base of the ... more

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2 ; Express 9 as an exponent of the base of the ... more

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3 ; Express 125 as an exponent of the base of the ... more

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6 ; Express 64 as an exponent of the base of the ... more

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; Express the decimal number as an equivalent ... more

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2 ; Express 100 as an exponent of the base of the ... more

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; Express 4 as in and rewrite as a negative ... more

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; Since , express 2 as an exponent of the base of... more

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0 ; Express 1 as an exponent of the base of the ... more

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1 ; Express as an exponent of the base of the ... more

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1 ; Express 10 as an exponent of the base of the ... more

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0 ; Express 1 as an exponent of the base of the ... more

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4 ; The exponent to which 5 must be raised to get... more

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; Rewrite the given radical in the form of an ... more

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; Rewrite the given radical in the form of an ... more

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; The exponent to which 10 must be raised to get... more

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; The exponent to which 10 must be raised to get... more

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0 ; Express 1 as an exponent of the base of the ... more

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; Since , express 7 as an exponent of the base of... more

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; The exponent to which 3 must be raised to get ... more

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; The exponent to which must be raised to get ... more

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; Rewrite the given radical in the form of an ... more

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0 ; Express 1 as an exponent of the base of the ... more

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; The exponent to which must be raised to get ... more

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; Rewrite the given radical in terms of an ... more

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; Since , express 4 as an exponent of the base of... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that, , where ... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Rewrite the given equation such that where is... more

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; Enter the given function into the graphing ... more

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; Enter the given function into the graphing ... more

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; Enter the given function into the graphing ... more

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; Enter the given function into the graphing ... more

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; Enter the given function into the graphing ... more

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; Enter the given function into the graphing ... more

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Does not exist ; Enter the given function into the... more

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; Enter the given function into the graphing ... more

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; Enter the given function into the graphing ... more

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Does not exist ; Enter the given function into the... more

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; Enter the given function into the graphing ... more

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; Enter the given function into the graphing ... more

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Does not exist ; Enter the given function into the... more

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Does not exist ; Enter the given function into the... more

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; Substitute 10 for , 4 for  , and 100 for  into ... more

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; Substitute 10 for , 3 for  , and 20 for  into ... more

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; Substitute 10 for , 100 for  , and  for  into ... more

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; Substitute 10 for , for  , and 100 for  into ... more

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; Substitute 10 for , 200 for , and 50 for into ... more

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; Substitute 10 for , for , and 1700 for into ... more

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; Substitute for , 3 for , and 12 for into the ... more

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; Substitute for , 4 for , and 25 for into the ... more

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; Substitute for , 100 for , and 15 for into ... more

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; Substitute for , 9 for , and 100 for into the... more

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Substitute different values of into the ... more

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Rewrite the given equation such that, , where is ... more

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Rewrite the given equation such that , where is ... more

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Substitute different values of into the ... more

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Shift left by 3 units from the graph of ; Domain:... more

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Shift right by 2 units in the graph of ; Domain: ... more

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Shift down by a unit from the graph of ; Domain: ... more

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Domain: ;Vertical Asymptote: ; The graph of the ... more

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Domain: ;Vertical Asymptote: ; The graph of the ... more

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 Domain: ;Vertical Asymptote: = 0 ; The graph of ... more

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Domain: ;Vertical Asymptote: ; The graph of the ... more

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Domain: ;Vertical Asymptote: ; The graph of the ... more

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 Domain: ;Vertical Asymptote: ; The graph of the ... more

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Domain: ;Vertical Asymptote: ; The graph of the ... more

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

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Substitute, , and for into function , and 0, 1, 2... more

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Slope:-intercept: ; Subtract from both sides of ... more

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0 ; Use the slope-intercept form, , where m is the... more

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Slope: Undefined-intercept: Not exist ; Substitute... more

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; Evaluate the value of the given function at. ; ... more

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; Evaluate the value of the given function at. ; ... more

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; The factors of the function are , , and .Let ... more

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; The factors of the function are , , and .Let ... more

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5 ; Apply the change of base formula in the given ... more

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; Apply the change of base formula to the given ... more

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; The domain is the set of values at which the ... more

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; The domain is the set of values at which the ... more

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; The domain is the set of values at which the ... more

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; The domain is the set of values at which the ... more

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; Consider the function .The equation becomes ... more

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; Take the function .The equation is equivalent ... more

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Take the function .Form a table for the function ... more

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The domain is the set of values at which the ... more

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Take an example of a one-to-one function, and it’s... more

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The - intercept is the point where , that is,the ... more

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One-to-one ; Substitute, , 1, and 2 for into the ... more

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Not one-to-one ; Substitute, , 1, and 2 for into ... more

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One-to-one ; Substitute, , 3, and 4 for into the ... more

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  ; Substitute for into the formula. Given:  ; ... more

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; Substitutefor into the given function. ; ... more

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Substitute 2 for into the given function and ... more

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; The interest is compounded quarterly, so the ... more

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0 ; The exponent to which 4 must be raised to ... more

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; Rewrite the base of the given logarithmic ... more

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; Express as an exponent of the base of the ... more

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2 ; Rewrite the base of the given logarithmic ... more

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0 ; The exponent to which must be raised to ... more

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; Express as an exponent of the base of the ... more

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0 ; The exponent to which 10 must be raised to ... more

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3 ; Express 27 as an exponent of the base of the ... more

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; Express as an exponent of the base of the ... more

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1 ; Rewrite as and the base of the given ... more

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; If , then . Use the statement in the given ... more

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; If , then . Use the statement in the given ... more

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; Rewrite the given expression with change of the... more

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; Rewrite the given expression with change of the... more

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As the given function is even, , this implies that... more

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Eighth ; Incase of compound interest, interest is ... more

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is a cubic function, while is an exponential ... more

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; Take logarithm on both sides and use the fact ... more

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; Apply the product rule, , to the given ... more

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; Apply the product rule, , to the given ... more

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; Apply the product rule, , to the given ... more

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; Apply the product rule, , to the given ... more

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; Use the product rule, in the given logarithm... more

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; Use the product rule, in the given logarithm... more

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; Use the product rule, in the given logarithm... more

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; Use the product rule, in the given logarithm... more

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; Use the power rule, in the given logarithm. ; more

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; Use the power rule, in the given logarithm. ; more

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; Use the power rule, in the given logarithm. ; more

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; Use the power rule, in the given logarithm. ; more

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; Use the power rule, in the given logarithm. ; more

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; Use the power rule, in the given logarithm. ; more

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; Write the given logarithm into exponential ... more

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; Write the given logarithm into exponential ... more

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; Use the quotient rule, , into the given ... more

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; Use the quotient rule, , into the given ... more

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; Use the quotient rule, , into the given ... more

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; Use the quotient rule, ,  in the given ... more

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; Use the quotient rule, , in the given logarithm... more

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; Use the quotient rule, , in the given logarithm... more

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; Use the product rule,, to simplify the given ... more

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; Use the product rule, , to simplify the given ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the rational exponent property, , to ... more

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; Apply the rational exponent property, , to ... more

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; Apply the rational exponent property, , to ... more

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; Apply the rational exponent property, , to ... more

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; Apply the rational exponent property, , to ... more

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; Use the power rule of logarithm, simplify the ... more

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; Use the product rule, , in the given logarithm... more

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1 ; Use the product rule, , in the given logarithm... more

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2 ; Use the quotient rule, , in the given ... more

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; Use the quotient rule, , in the given logarithm... more

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; Use the power rule, , in the given logarithm... more

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; Use the power rule, , in the given logarithm... more

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; Apply the power rule, , to simplify the given ... more

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; Apply the power rule, , in the given expression... more

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; Apply the power rule, , in the given logarithm ... more

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; Apply the quotient rule, ,  in the given ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the quotient rule of logarithm in the ... more

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; Apply the product rule of logarithm on the term... more

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; Apply the quotient rule of logarithm on the ... more

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; Express 4 as in the given expression.Apply the ... more

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; Apply the product rule of logarithm in the ... more

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; Apply the quotient rule of logarithm in the ... more

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; Express 14 as a product of 2 and 7 in the given... more

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; Express 98 as a product of 2 and in the given ... more

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; Apply the quotient rule of logarithm in the ... more

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; Substitute for and for into the given ... more

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Not possible ; The value  cannot be written in the... more

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; Express 125 as in the given expression.Apply ... more

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; Apply the quotient rule of logarithm to the ... more

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; Apply the quotient rule of logarithm to the ... more

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; Express 30 as the product of 6 and 5 in the ... more

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; Apply the quotient rule of logarithm to the ... more

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; Express as the product of 15 and in the given... more

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3 ; The base of logarithm and the variable raised ... more

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2713 ; The base of the logarithm and the variable ... more

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; The base of the logarithm and the variable ... more

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; The base of the logarithm and the variable ... more

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; The power of 3 has a logarithm whose base is ... more

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; The power of 5 has a logarithm whose base is ... more

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; Rewrite the given expression by taking the base... more

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; Rewrite the given expression by taking the base... more

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; Rewrite the given expression by taking the base... more

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; Rewrite the given expression by taking the base... more

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; Apply the rational exponent property to ... more

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; Apply the rational exponent property to ... more

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Linear:; Quadratic: Cubic: Quartic: Rational:; ... more

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; Apply the property on the left side of given ... more

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; Apply the property on the left side of given ... more

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; Apply the product rule for logarithms in the ... more

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; Apply the quotient rule for the given ... more

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; Apply the rational exponent property, , to ... more

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; Apply the rational exponent property, , to ... more

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; Apply the property of radicals into the given ... more

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False ; Assess the left side of the given equation... more

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True ; Assess the right side of the given equation... more

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False ; Substitute for and for into the left ... more

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True ; Take the left side of the given equation.... more

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True ; Take the left side of the given expression.... more

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True ; Take the left side of the given equation.... more

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True ; Take the left side of the given equation.... more

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; Rewrite  as  in the given expression and then ... more

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; Apply the change of base formula in the given ... more

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3 ; Apply the change of base formula in the given ... more

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

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

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Entire Proof Answer:Take left side of the given ... more

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Entire Proof Answer:Take left side of the given ... more

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4 ; Rewrite 81 as in the given equation. ; Use ... more

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