Rewrite the logarithm $\log _ { 4 } 25$ in terms of the natural logarithm.
A) $\frac { \ln 25 } { \ln 4 }$
B) $\frac { \ln 4 } { \ln 25 }$
C) $\ln 4 \ln 25$
D) $\frac { \ln 25 } { \log _ { 4 } e }$
E) $\ln 25$

Question

Quizplus · Accepted Answer

We can use the change of base formula for logarithms to rewrite $\log _ { 4 } 25$ in terms of natural logarithms. 
\begin{align*}
\log _ { 4 } 25 &= \frac{\ln 25}{\ln 4} &\text{(change of base formula)}\
&= \ln 25 \cdot \frac{1}{\ln 4} &\text{(reciprocal property)}\
&= \frac{\ln 25}{\ln 4} &\text{(simplify)}
\end{align*}
So the answer is A).

Rewrite the Logarithm log⁡425\log _ { 4 } 25log4​25 In Terms of the Natural Logarithm

Rewrite the Logarithm $\log _ { 4 } 25$ In Terms of the Natural Logarithm