# How do you calculate log_(1/6) 216?

May 4, 2016

Use the change of base rule ${\log}_{a} n = \log \frac{n}{\log} a$

#### Explanation:

$= \log \frac{216}{\log} \left(\frac{1}{6}\right)$

$= \log \frac{{6}^{3}}{\log} \left({6}^{-} 1\right)$

Use the rule $\log {a}^{n} = n \log a$

$= \frac{3 \log 6}{- 1 \log 6}$

$= - 3$

Hopefully this helps!