# How do you calculate log_(1/5) 125?

Apr 18, 2016

First, use the change of base rule ${\log}_{a} n = \log \frac{n}{\log} a$

#### Explanation:

${\log}_{\frac{1}{5}} \left(125\right)$

$\to \log \frac{125}{\log} \left(\frac{1}{5}\right)$

$\to \log \frac{{5}^{3}}{\log} \left({5}^{-} 1\right)$

Now, use the following log rule: $\log {n}^{a} = a \log n$

$\to \frac{3 \log 5}{- 1 \log 5}$

$\to - 3$

Thus, ${\log}_{\frac{1}{5}} \left(125\right) = - 3$

Hopefully this helps!