[tex]\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 2\log_2(x)+\log_2(x+5)\implies \log_2(x^2)+\log_2(x+5) \\\\\\ \log_2[x^2(x+5)]\implies \log_2(x^3+5x^2)[/tex]
