Answer
-2.0478
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, $log_{\frac{1}{5}}27=x$ means the same as $\frac{1}{5}^{x}=27$.
By using a calculator to approximate, we know that $x=-2.0478$, because $\frac{1}{5}^{-2.0478}=27$.
