[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 rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \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}[/tex][tex]\log_3(v)-4\log_3(w)\implies \log_3(v)-\log_3(w^4)\implies \log_3\left( \cfrac{v}{w^4} \right) \\\\[-0.35em] ~\dotfill\\\\ \log_4(n\sqrt{m})\implies \log_4(n)+\log_4(\sqrt{m}) \\\\\\ \log_4(n)+\log_4\left( m^{\frac{1}{2}} \right) \implies \log_4(n)+\cfrac{1}{2}\log_4(m)~~\textit{\large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{cd^3}{e^4} \right)\implies \underline{\log_2(cd^3)}-\log_2(e^4) \\\\\\ \underline{\log_2(c)+\log_2(d^3)}-\log_2(e^4) \implies \log_2(c)+3\log_2(d)-4\log_2(e)[/tex]
