#### Answer

$log_{8}\frac{1}{4}=-\frac{2}{3}$

#### Work Step by Step

For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $8^{-\frac{2}{3}}=\frac{1}{4}$ means the same as $log_{8}\frac{1}{4}=-\frac{2}{3}$.