Answer
$\log_{7}9=\frac{2A}{B}$
Work Step by Step
The change of base property states that:
For any logarithmic bases $a$ and $b,$ and any positive number $M$.
$\log_{b}M=\frac{\log_{a}M}{\log_{a}b},$
The logarithm of $M$ with base $b$ is equal to the logarithm of $M$ with any new base divided by the logarithm of $b$ with that new base.
Therefore we have:
$\log 3=A, \log 7=B.$
$\log_{7}9=\log_{7}3^2=2\log_{7}3=2\left(\frac{\log_{10}3}{\log_{10}7}\right)=\frac{2A}{B}$
