## Precalculus: Mathematics for Calculus, 7th Edition

$- \frac {3}{2}$
$\log_5 \frac{1}{\sqrt {125}}$ Rewrite the square root to exponential form $\log_5 \frac{1}{125^{\frac{1}{2}}}$ 125 = $5^{3}$ since 5 $\times$ 5 $\times$ 5 = 125. $\log_5 \frac{1}{(5)^{{3}^{\frac{1}{2}}}}$ When there's a base to a power times a power, we multiply the powers together $\log_5 \frac{1}{5^{\frac{3}{2}}}$ We can move the denominator to the numerator by changing the power to a negative $\log_5 5^{- \frac{3}{2}}$ = $- \frac {3}{2}$