Algebra and Trigonometry: Real Mathematics, Real People (7th Edition)

Chapter 5

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; Substitute for in the given function,   to ... more

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Use the given functions, , and to draw a table by... more

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Use the given functions, , and to draw a table by... more

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; Enter the expression in the graphing utility... more

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Use the function, , to draw a table by ... more

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; Write the formula for the balance with ... more

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  ; Write the equation representing the quantity ... more

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The functions , , and approach infinity as ... more

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The transformation is . ; Observe the table given ... more

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; Enter the equations into the graphing utility... more

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As , the function ; Yes, there is -intercept; In ... more

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The graph of is obtained by shifting the graph of... more

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Transcendental ; A function which is non-algebraic... more

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Natural exponentialNatural  ; The function in the ... more

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Horizontal shift one unit to the left. ; Replacing... more

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Compound interest ; If the principal is amounted ... more

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; Substitute for into the given function to ... more

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; Substitute for into the given function to ... more

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; Substitute for into the given function to ... more

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

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Horizontal asymptote  at   ; Use the given ... more

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Horizontal asymptote  at ; Use the given function... more

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Horizontal asymptote  at ; First, use the property... more

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Horizontal asymptote  at ; First, use the property... more

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Horizontal asymptote  at ; Use the given function... more

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Horizontal asymptote  at ; Use the given function ... more

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Horizontal asymptote  at ; First, use the property... more

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Horizontal asymptote  at ; First, use the property... more

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Sketch the graph the given functions, and . ; ... more

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Sketch the graph the given functions, and . ; ... more

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Sketch the graph the given functions, and . ; ... more

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Sketch the graph the given functions and . ; From... more

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The graph has a horizontal shift of five units to ... more

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The graph has a horizontal shift of four units to ... more

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The graph of is obtained by shifting the graph of... more

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The graph of is obtained by shifting the graph of... more

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The graph of is obtained by shifting the graph of ... more

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The graph of is obtained by reflecting the graph ... more

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The graph of is obtained by shifting the graph of... more

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The graph of is obtained by shifting the graph of ... more

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 The graph of is obtained by reflecting the graph... more

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 The graph of is obtained by shifting the graph ... more

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; Take the given function and find the value of ... more

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; Take the given function and find the value of ... more

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; Take the given function and find the value of ... more

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; Take the given function and find the value of ... more

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 0121 ; Asymptote: ; Enter the function, , in the ... more

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 0121 ; Asymptote: ; Enter the function, , in the ... more

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 0121636 ; Asymptote: ; Enter the function, , in ... more

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 0123124 Asymptote: ; Enter the function, , into ... more

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 0113927Asymptote: ; Enter the function, , into ... more

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 0121Asymptote: ; Enter the function, , into the ... more

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 012324Asymptote: ; Enter the function, , into the... more

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 01214Asymptote: ; Enter the function, , into the ... more

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 0121Asymptote: ; Enter the function, , into the ... more

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 0123  ; Asymptote: ; Enter the function, , into ... more

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 3Asymptote: ; Enter the function, , into the CAS ... more

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 012342Asymptote: ; Enter the function, , into the... more

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 345673Asymptote: ; Enter the function, , into the... more

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 013Asymptote: ; Enter the function, , into the ... more

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 0212Asymptote: ; Enter the function, , into the ... more

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 0012Asymptote: ; Enter the function, , into the ... more

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

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

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

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

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 124 12365Continuous  ; Use the formula of ... more

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 124 12365Continuous  ; Use the formula of ... more

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 124 12365Continuous ; Use the formula of compound... more

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 124 12365Continuous ; Use the formula of compound... more

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 11020 304050  ; Use the formula for the balance... more

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 11020 304050  ; Use the formula for the balance... more

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 11020 304050  ; Use the formula for the balance... more

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 11020 304050 ; Use the formula for the balance ... more

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; Substitute 25 for , for , and 48 for into the... more

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; Substitute 100 for , for , and 60 for into ... more

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; Substitute 200 for , for , and 72 for into ... more

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; Substitute 75 for , for , and 24 for into the... more

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TrueThe base of an exponential function cannot be ... more

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 FalseThe number is an irrational number. ;  ... more

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The given graph should be a graph of an ... more

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; Enter the equations into the graphing utility ... more

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; The graph (a) is decreasing from left to right ... more

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>  ; Find the value of the number, , on the left ... more

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; Find the value of the number on the left side... more

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; Find the value of the number on the left side... more

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; Find the value of the number on the left side... more

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; Plot the graph of the given function and check ... more

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; Plot the graph of the given function and check ... more

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; Plot the graph of the given function and check ... more

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The given function is not one-to-one function, and... more

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Construct a table by taking simple values of .Then... more

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Tabulate the value of  for different value of... more

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; Domain of the logarithmic function is defined ... more

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; Enter the equations and into the CAS to ... more

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Logarithm ; Every exponential function can be ... more

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Common ; The function that has base 10 is known as... more

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  ; The inverse property of logarithm function ... more

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; According to the definition of natural ... more

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; Write the definition of logarithmic function ... more

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; Write one-to-one property of logarithmic ... more

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; Write the definition of logarithmic function ... more

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; Write the definition of logarithmic function ... more

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; Write the definition of logarithmic function ... more

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; Write the definition of logarithmic function ... more

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; Write the definition of logarithmic function ... more

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; Write the definition of logarithmic function ... more

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; Write the definition of logarithmic function ... more

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; Write the definition of logarithmic function ... more

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; The exponential function is written as an ... more

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; The exponential function is written as an ... more

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; The exponential function is written as an ... more

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; The exponential function is written as an ... more

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; The exponential function is written as an ... more

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; The exponential function is written as an ... more

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; The exponential function is written as an ... more

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; The exponential function is written as an ... more

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; Substitute the value of in the given function... more

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; Substitute for in the given function... more

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

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; Substitute for in to evaluate this function... more

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; Enter the value for in the function in the ... more

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; Enter the value for in the function in the ... more

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; Enter the value for in the function in  the ... more

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; Enter the value for in the function in  the ... more

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; Use the one to one property . It states that if... more

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; Use the one to one property . It states that if... more

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; Use the  inverse property to solve the equation... more

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; Use the  inverse property to solve the equation... more

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; Use the one to one property . It states that if... more

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; Use the one to one property . It states that if... more

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; Use the inverse property to solve the equation... more

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; Use the inverse property to solve the equation... more

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; Write the logarithmic expression as .Use the ... more

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; Write the logarithmic expression as . Use the ... more

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The table of values for the function   is:  Plot ... more

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The table of values for the function   is:   Plot ... more

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The table of values for the function   is:   Plot ... more

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The table of values for the function   is:   Plot ... more

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The domain of the function  is .The Vertical ... more

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The domain of the function  is .The Vertical ... more

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The domain of the function  , is .The vertical ... more

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The domain of the function  , is .The vertical ... more

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The domain of the function  , is .The vertical ... more

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The domain of the function  , is .The vertical ... more

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For the function , the asymptote: ; domain: ; and ... more

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For the function , the vertical asymptote: ; ... more

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For the function , the vertical asymptote: ; ... more

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For the function , the asymptote: ; domain: ; and ... more

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The graph of the function is a reflection of the ... more

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The graph of the function is a horizontal shift ... more

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The graph of the function is a reflection on the... more

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The graph of the function is a vertical shift of ... more

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The graph of the function is a horizontal shift ... more

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The graph of the function is a horizontal shift ... more

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; The logarithmic and exponential functions are ... more

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; The logarithmic and exponential functions are ... more

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; The logarithmic and exponential functions are ... more

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; The logarithmic and exponential functions are ... more

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; The logarithmic and exponential functions are ... more

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; The logarithmic and exponential functions are ... more

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; The logarithmic and exponential functions are ... more

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; The logarithmic function and exponential ... more

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; The exponential functions and logarithmic ... more

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; The exponential functions and logarithmic ... more

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; The exponential functions and logarithmic ... more

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; The exponential functions and logarithmic ... more

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; The exponential functions and logarithmic ... more

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; The exponential functions and logarithmic ... more

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; The exponential functions and logarithmic ... more

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; The exponential functions and logarithmic ... more

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

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

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0.693 ; Enter the given function in the graphing ... more

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-0.649 ; Enter the given function in the graphing ... more

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2 ; Use the inverse property of natural ... more

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-1 ; Use the inverse property of natural ... more

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1.8 ; Use the inverse property of natural ... more

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0 ; Use the property of natural logarithms.... more

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0 ; Use the property of natural logarithms.... more

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22 ; Use the inverse property of natural ... more

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1 ; Use the property of natural logarithms.... more

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-4 ; Use the inverse property of natural ... more

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Logarithmic function is defined for only positive ... more

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   ; The function is defined when is greater than... more

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Domain: Vertical asymptote: -intercept: ; The ... more

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Domain: Vertical asymptote: -intercept: ; The ... more

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The graph of is a horizontal shift of eight units... more

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The graph of is a horizontal shift of  4 units to... more

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The graph of is obtained by shifting the graph of... more

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The graph of is obtained by shifting the graph of... more

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The graph of is obtained by shifting the graph of... more

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The graph of is obtained by shifting the graph of... more

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False, the graph of function can be obtained by ... more

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True, the point lies on the graph of function... more

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2 ; Substitute 32 for x and 5 for into the given ... more

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3 ; Substitute 81 for and 4 for   into the given ... more

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

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; Substitute for and 3 for into the given ... more

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The graph is obtained by shifting the graph of the... more

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The graph is obtained by shifting the graph of the... more

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The logarithmic function is the inverse function ... more

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monthsSubstitute 60 for to determine the value of... more

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; Rewrite the middle  term  2x of the given ... more

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; Rewrite the middle term 4x of the given ... more

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; Factor the polynomial by splitting the middle ... more

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; Factor the polynomial by splitting the middle ... more

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; Rewrite the given polynomial. ; Simplify using ... more

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; Rewrite the given polynomial. ; Simplify using ... more

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; Take out as a common factor. ; Factor the ... more

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; Take out as a common factor. ; Factor the ... more

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15 ;  Find the function by substituting and .... more

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1 ; Find the function  by substituting  and .... more

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No solution ;  No solution ; Enter the equations... more

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; Enter the equations, and  in the graphing ... more

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; Enter equations, and , in the graphing utility... more

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No solution ; Enter equations,  and , in the ... more

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; For to be a positive real number and , the ... more

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; For to be a positive real number and , the ... more

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Apply the power property of logarithms,Simplify ... more

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; Use rational exponents and rewrite the radical ... more

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; Expand the parenthesis using the power property... more

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; Tabulate by taking the natural log of values of... more

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The domains of two functions are different. ; Use ... more

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Change-of-base ; For , , and to be positive real ... more

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; The product of a real number and logarithm of ... more

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is correct as the change of base formula is ... more

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The quotient property of logarithms is to be used ... more

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approximately ; For to be a positive real number ... more

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approximately ; For to be a positive real number ... more

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; For to be a positive real number and , the ... more

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; For to be a positive real number and , the ... more

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approximately ; For to be a positive real number ... more

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approximately ; For to be a positive real number ... more

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approximately ; For to be a positive real number ... more

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approximately ; For to be a positive real number... more

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; Rewrite 20  as a product of 4 and 5. ; Apply ... more

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; Rewrite 500 as a product of 4 and 125. ; ... more

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; Apply the quotient property of logarithms and ... more

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; Apply the quotient property of logarithms and ... more

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; Rewrite 8 as a cube of 2, that is, in the ... more

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; Rewrite 30 as a product of 2, 3 and 5 in the ... more

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; Apply the quotient property of logarithms and ... more

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; Rewrite the radical as  rational exponent and ... more

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The graph for the given function is as follows, ; ... more

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The graph for the given function is as follows, ; ... more

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The graph for the given function is as follows, ; ... more

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The graph for the given function is as follows, ; ... more

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The graph for the given function is as follows, ; ... more

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The graph for the given function is as follows... more

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The graph for the given function is as follows, ; ... more

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The graph for the given function is as follows, ; ... more

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; Rewrite 8 as and apply the power property of ... more

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; Rewrite 243 as a product of 81 and 3, and apply... more

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; Apply the product and power properties of ... more

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; Apply the product property of logarithms and ... more

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; Apply the product and power properties of ... more

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; Apply the product property of logarithms and ... more

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; Apply the quotient property of logarithms and ... more

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; Apply the quotient property of logarithms and ... more

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Apply the quotient property of logarithms and ... more

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Rewrite 24 as a product of and 3, and apply the ... more

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; Apply the product property of logarithms and ... more

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; Apply the product property of logarithms and ... more

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; Apply the quotient property of logarithms, . ... more

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; Apply the quotient property of logarithms. .... more

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; Apply the power property of logarithms, which ... more

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; Apply the power property of logarithms, which ... more

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; Rewrite the radical as rational exponent in the... more

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; Rewrite the radical as rational exponent in the... more

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; Apply the product property of logarithms, which... more

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; Apply the quotient property of logarithms and ... more

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; Apply the product property of logarithms and ... more

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; Apply the product property of logarithms and ... more

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; Rewrite the radical as rational exponent in the... more

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; Rewrite the radical as rational exponent in the... more

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; Apply the property of difference between the ... more

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; Apply the quotient property of logarithms and ... more

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; Apply the quotient property of logarithms. ; ... more

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; Apply the quotient property of logarithms. ; ... more

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; Apply the product property of logarithms, that ... more

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; Apply the product property of logarithms, that ... more

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; Apply the quotient property of logarithms, that... more

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; Apply the quotient property of logarithms, that... more

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; Apply the power property of logarithms, that is... more

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; Apply the power property of logarithms, that is... more

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; Apply the power property of logarithms on the ... more

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; Apply the power property of logarithms on the ... more

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; Apply the power property of logarithms on the ... more

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; Apply the power property of logarithms on the ... more

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; Apply the power property of logarithms on the ... more

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; Use the power property of logarithms on the ... more

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; Use the product property of logarithms on the ... more

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; Use the product property of logarithms on the ... more

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; Use the power property of logarithms in the ... more

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; Use the quotient property of logarithms on the ... more

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2 ; Express 9 as the square of 3, that is, and ... more

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1 ; The logarithm with base of number is equal ... more

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; Express 16 as the square of 4, that is, . Also... more

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; Express 125 as the cube of 5, that is, such ... more

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Not defined ; Logarithm is defined for all the ... more

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Not defined ; Logarithm is defined for all the ... more

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3 ; Apply the quotient property of the logarithm ... more

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3 ; Apply the product property of the logarithm ... more

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; Apply the power property of the logarithm. ; ... more

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; Apply the power property of the logarithm. ; ... more

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8 ; Apply the power property of the logarithm. ; ... more

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15 ; Apply the power property of the logarithm. ; ... more

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; Express the radical in the denominator of the ... more

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; Express the radical in the expression as a ... more

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; Take natural log of x and y values to find the ... more

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The transformed equations show direct or inverse ... more

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True  ; According to the product property of ... more

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False ; For a function consider and . For the ... more

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FalsePower property of logarithm is applied on the... more

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FalsePower property of logarithm is applied on the... more

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TrueFor value of to be which if is negative, ... more

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False ; For a function, Let  . Then,Therefore, ... more

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The quotient property of logarithms is not applied... more

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The functions and have the same graph. ; After ... more

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14 integersLogarithmic functionApproximate value0... more

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The graph of logarithmic function has a zero value... more

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The two functions have different domains. ; The ... more

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Entire Proof Answer: Let and Take exponent with ... more

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; Use the property of exponents  ; Express eight ... more

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; Use the property of exponents  ; Use the ... more

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; Use the property of exponents  ; Use the ... more

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; Use the property of exponents  ; Use the ... more

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0The value of is equal to . ; Enter the given ... more

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; Subtract four from each side in the given ... more

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; Rewrite the equation in quadratic form.  ; To ... more

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

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

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10 ; Use the product property logarithms. ; ... more

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Entire Proof Answer: Consider the left side of the... more

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   ; Enter the equation, in CAS to obtain the ... more

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years ; Assume that the deposited amount is and ... more

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2008 ; Average salary for public school teacher ... more

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Extraneous  ; Consider the  logarithmic equation: ... more

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7 ; Use the inverse property of logarithms to ... more

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Yes  ; Write for 125 in the equation, .Use one to... more

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Subtract three from each side of the equation. ; ... more

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Inverse property ; Use the inverse property to ... more

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; Enter the equation and into CAS to obtain the... more

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; Enter the equation, into CAS to obtain the ... more

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; Enter the equation, into CAS to obtain the ... more

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; Enter the equation, into CAS to obtain the ... more

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; Enter the equation, into CAS to obtain the ... more

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; Enter the equation, into CAS to obtain the ... more

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; Enter the equation, into CAS to obtain the ... more

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; Enter the equation, ,and into CAS to obtain ... more

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4 ; Rewrite 16 in exponential form with base four... more

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5 ; Rewrite 243 in exponential form with base ... more

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; Rewrite in exponential form with base five. ; ... more

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; Rewrite in exponential form with base seven... more

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; Rewrite in exponential form with base eight... more

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; Rewrite in exponential form with base two. ; ... more

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; Rewrite ,where 81 is in exponential form with ... more

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; Rewrite ,where 64 is in exponential form with ... more

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; Apply natural logarithm on both sides of ... more

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; Apply the natural logarithm on both sides of ... more

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; Divide by six on both sides of equality. ; ... more

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; Divide both sides by five. ; Apply the ... more

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5 ; Rewrite 256 in exponential form with base two... more

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; Rewrite the equation. ; Use one-to-one property... more

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; Add to each side of the equation. ; Use one-to... more

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; Add to each side of the equation. ; Use one-to... more

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; Exponentiate each side of the equation. ; Use ... more

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; Exponentiate each side of the equation. ; Use ... more

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; Use the change of base property and rewrite the... more

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; Use change of base property and rewrite the ... more

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; Use change of base property and rewrite the ... more

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; Write the given equation in exponential form ... more

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; Exponentiate the given equation on both sides ... more

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; Exponentiate the given equation on both sides ... more

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; Rewrite the given expression. ; Compare the ... more

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; Write in terms of to rearrange the expression... more

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; Write in terms of to rearrange the expression... more

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; As (natural log) is equal to , use it to ... more

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; Use the inverse property to rewrite the given ... more

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; Use the inverse property to rewrite the given ... more

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; Use the inverse property  and solve. ; ... more

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; Use the inverse property and solve. ; Simplify... more

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  ; Take logarithm on both sides. ;   ; Using the ... more

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0.894 ; Take the natural log of both sides of the ... more

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2 ; Take the natural log of both sides of the ... more

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; Take the natural log of both sides of the ... more

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; Divide both sides of the equation by 250. ; ... more

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; Divide both sides of the equation by 100. ; ... more

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; Divide both sides of the equation by 500. ; ... more

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; Divide both sides of the equation by 1000. ; ... more

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; Add to both sides of the equation and simplify... more

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; Add 14 to both sides of the equation and ... more

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; Add 13 to both sides of the equation and ... more

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; Subtract 15 from both sides of the equation and... more

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; Rewrite the equation after simplification. ; ... more

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