TeX source:

\begin{aligned} \log _{b}(M N) &=\log _{b}\left(b^{m} b^{n}\right) & & \text { Substitute for } M \text { and } N\\ &=\log _{b}\left(b^{m+n}\right) & & \text { Apply the product 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 \text {. } \end{aligned}