[tex]\bf \textit{logarithm of factors}\\\\
log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)
\\\\\\
\textit{Logarithm of rationals}\\\\
log_{{ a}}\left( \frac{x}{y}\right)\implies log_{{ a}}(x)-log_{{ a}}(y)
\\\\\\
\textit{Logarithm of exponentials}\\\\
log_{{ a}}\left( x^{{ b}} \right)\implies {{ b}}\cdot log_{{ a}}(x)\\\\
-------------------------------[/tex]
[tex]\bf log(m^3n)\implies log(m^3)+log(n)\implies 3log(m)+log(n)
\\\\\\
\boxed{3k+v}
\\\\\\
log\left(\cfrac{m}{n^3} \right)\implies log(m)-log(n^3)\implies log(m)-3log(n)
\\\\\\
\boxed{k-3v}[/tex]
