Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms. $y = \log _ { 4 } x$
A) $y = 4 \ln x$
B) $y = \ln ( x - 4 )$
C) $y = \ln x - \ln 4$
D) $y = 4 ^ { x }$
E) $y = \frac { \ln x } { \ln 4 }$

Question

Quizplus · Accepted Answer

The change-of-base formula for logarithms states that $\log_b a = \frac{\log_c a}{\log_c b}$, where $b$ and $c$ are bases and $a$ is the argument of the logarithm. Applying this formula to $\log_4 x$ with the natural logarithm (base $e$) gives $y = \frac{\ln x}{\ln 4}$, which matches choice E.

Use a Change-Of-Base Formula to Rewrite the Logarithm in Terms y=log⁡4xy = \log _ { 4 } xy=log4​x

Use a Change-Of-Base Formula to Rewrite the Logarithm in Terms $y = \log _ { 4 } x$