Answer
$log_{8}\frac{15}{4}$
Work Step by Step
We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{8}5+log_{5}15-log_{8}20=log_{8}(5\times15)-log_{8}20=log_{8}75-log_{8}20$.
We know that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{8}75-log_{8}20=log_{8}\frac{75}{20}=log_{8}\frac{75\div5}{20\div5}=log_{8}\frac{15}{4}$.
