# How do you expand log (6/5)^6?

Aug 12, 2018

$\log {\left(\frac{6}{5}\right)}^{6} = 6 \log 6 - 6 \log 5$

#### Explanation:

As $\log \left(\frac{a}{b}\right) = \log a - \log b$ and $\log {a}^{m} = m \log a$

hence $\log {\left(\frac{6}{5}\right)}^{6}$

= $6 \log \left(\frac{6}{5}\right)$

= $6 \left(\log 6 - \log 5\right)$

= $6 \log 6 - 6 \log 5$