[tex]\begin{array}{llll} \textit{Logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \ln\left[ z(z-1)^9 \right]\implies \ln(z)~~ + ~~\ln[(z-1)^9]\implies \ln(z)~~ + ~~9\ln[(z-1)][/tex]
