Algebra and Trigonometry: Real Mathematics, Real People (7th Edition)
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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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is the actual solution; is not the solution. ; ... more
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years ; First, find the radioactive decay rate ... more
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Exponential growth function is defined as,Consider... more
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1$10,832.8710$22,255.4120$49,530.3230$110,231.7640... more
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1$10,304.5510$13,498.5420$18,221.1930$24,596.6340$... more
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012101 ; Horizontal asymptote: -intercept : ; ... more
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; Apply the power property, , to simplify the ... more
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; Divide both sides of the given equation by 8... more
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; Add 29 to both sides of the equation. ; Apply ... more
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; Apply the product rule of logarithms to the ... more
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; Divide both sides of the given equation by . ; ... more
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0; 1 ; Factor out from the given equation. ; ... more
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No solution ; Apply the division property of ... more
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; ; ; ; Substitute in average cost formula. ; ... more
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