Answer
$log_{8}\frac{15}{4}$
Work Step by Step
The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{8}5+log_{8}15-log_{8}20= log_{8}(5\times15)-log_{8}20= log_{8}75-log_{8}20$.
The quotient property of logarithms tells us 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{15}{4}$.
