TeX source:

\begin{aligned} \log _{b}\left(\frac{A}{C}\right) &=\log _{b}\left(A C^{-1}\right) \\ &=\log _{b}(A)+\log _{b}\left(C^{-1}\right) \\ &=\log _{b} A+(-1) \log _{b} C \\ &=\log _{b} A-\log _{b} C \end{aligned}