# How do you expand ln(8^5/7)^4?

Feb 15, 2017

$\ln {\left({8}^{5} / 7\right)}^{4} = 20 \ln 8 - 4 \ln 7$

#### Explanation:

We can use the identities $\ln {a}^{b} = b \ln a$ and $\ln \left(\frac{a}{b}\right) = \ln a - \ln b$

Hence $\ln {\left({8}^{5} / 7\right)}^{4}$

= $4 \ln \left({8}^{5} / 7\right)$

= $4 \left(\ln {8}^{5} - \ln 7\right)$

= $4 \left(5 \ln 8 - \ln 7\right)$

= $20 \ln 8 - 4 \ln 7$