Answer
$C-A$
Work Step by Step
We are given that $log_{b}2=A$ and $log_{b}3=C$.
Based on the quotient rule of logarithms, we know that $log_{b}(\frac{M}{N})=log_{b}M-log_{b}N$ (where $b$, $M$, and $N$ are positive real numbers and $b\ne1$).
Therefore, $log_{b}\frac{3}{2}=log_{b}3-log_{b}2=C-A$.