Use the change of base formula to identify the expression that is equivalent to $\log _ { 9 } 7$ .
A) $\frac { \log 7 } { \log 9 }$
B) $\frac { \log 9 } { \log 7 }$
C) $\frac { \ln 9 } { \ln 7 }$
D) $9 \log 7$

Question

Quizplus · Accepted Answer

The change of base formula states that $\log_a b=\frac{\log_c b}{\log_c a}$ for any positive real numbers $a, b,$ and $c
eq1$ where $c$ is the base we want to convert to. In this case, we want to change $\log_9 7$ to $\log 7$ (since $\log$ usually implies the base 10 logarithm). Therefore, we have $\log_9 7=\frac{\log 7}{\log 9}$, which is equivalent to choice $\boxed{	extbf{(A)}}$.

Use the Change of Base Formula to Identify the Expression log⁡97\log _ { 9 } 7log9​7

Use the Change of Base Formula to Identify the Expression $\log _ { 9 } 7$