Answer
$\displaystyle \log_{5}\frac{1}{25}=-2$
Work Step by Step
$\log_{b}x=y $ is equivalent to $ b^{y}=x $
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$\displaystyle \log_{5}\frac{1}{25}=y \quad $ is equivalent to $ \quad 5^{y}=\displaystyle \frac{1}{25}$
Since $ \quad 5^{-2}=\displaystyle \frac{1}{5^{2}}=\frac{1}{25},$
it follows that $ \quad y=-2,\ \quad $ so
$\displaystyle \log_{5}\frac{1}{25}=-2$
