TeX source:

\begin{aligned} \log _{b}\left(\frac{M}{N}\right) &=\log _{b}\left(\frac{b^{m}}{b^{n}}\right) & & \text { Substitute for } M \text { and } N . \\ &=\log _{b}\left(b^{m-n}\right) & & \text { Apply the quotient rule for exponents. } \\ &=m-n & & \text { Apply the inverse property of logs. } \\ &=\log _{b}(M)-\log _{b}(N) & & \text { Substitute for } m \text { and } n . \end{aligned}