Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.

f ( x ) = \log _ { \frac { 1 } { 5 } } x

f ( x ) = \frac { \log \frac { 1 } { 5 } } { \log x } = \frac { \ln \frac { 1 } { 5 } } { \ln x }

$Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio. f ( x ) = \log _ { \frac { 1 } { 5 } } x A) f ( x ) = \frac { \log \frac { 1 } { 5 } } { \log x } = \frac { \ln \frac { 1 } { 5 } } { \ln x } B) f ( x ) = \frac { \log x } { \log \frac { 1 } { 5 } } = \frac { \ln x } { \ln \frac { 1 } { 5 } } C) f ( x ) = \log x + \log \frac { 1 } { 5 } = \ln x + \ln \frac { 1 } { 5 } D) f ( x ) = \log \frac { \frac { 1 } { 5 } } { x } = \ln \frac { \frac { 1 } { 5 } } { x } E) f ( x ) = \log \frac { x } { \frac { 1 } { 5 } } = \ln \frac { x } { \frac { 1 } { 5 } }$
B)

f ( x ) = \frac { \log x } { \log \frac { 1 } { 5 } } = \frac { \ln x } { \ln \frac { 1 } { 5 } }

f ( x ) = \log x + \log \frac { 1 } { 5 } = \ln x + \ln \frac { 1 } { 5 }

f ( x ) = \log \frac { \frac { 1 } { 5 } } { x } = \ln \frac { \frac { 1 } { 5 } } { x }

f ( x ) = \log \frac { x } { \frac { 1 } { 5 } } = \ln \frac { x } { \frac { 1 } { 5 } }

Solve the Logarithmic Equation Algebraically 2log⁡3(0.5x)=52 \log _ { 3 } ( 0.5 x ) = 52log3​(0.5x)=5

Multiple Choice

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Solve the Logarithmic Equation Algebraically $2 \log _ { 3 } ( 0.5 x ) = 5$

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