[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)\\\\
-------------------------------\\\\
log_3\left( \cfrac{2r^5}{y^8} \right)\implies log_3(2r^5)-log(y^8)
\\\\\\
\boxed{log_3(2)+log_3(r^5)}-log_3(y^8)\implies log_3(2)+5log_3(r)-8log_3(y)[/tex]
