Question

Expand the logarithmic expression. I will award brainliest.

Answer 1

$\bf \textit{logarithm of factors}\\\\ log_a(xy)\implies log_a(x)+log_a(y) \\\\\\ \textit{Logarithm of rationals}\\\\ log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y) \\\\\\ \textit{Logarithm of exponentials}\\\\ log_a\left( x^ b \right)\implies b\cdot log_a(x)\\\\ -------------------------------\\\\ log_3\left( \cfrac{2r^5}{y^8} \right)\implies log_3(2r^5)-log(y^8) \\\\\\ \boxed{log_3(2)+log_3(r^5)}-log_3(y^8)\implies log_3(2)+5log_3(r)-8log_3(y)$