Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3 - Page 477: 83

$C-A$

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, $log_{b}\frac{3}{2}=log_{b}3-log_{b}2=C-A$.