# How do you simplify ln 3 − 2(ln 4 + ln 8)?

May 24, 2018

$\ln 3 - 2 \left(\ln 4 + \ln 8\right) = \ln \left(\frac{3}{1024}\right)$

#### Explanation:

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

Hence $\ln 3 - 2 \left(\ln 4 + \ln 8\right)$

= $\ln 3 - 2 \ln \left(4 \cdot 8\right)$

= $\ln 3 - 2 \ln 32$

= $\ln 3 - \ln \left({32}^{2}\right)$

= $\ln \left(\frac{3}{32} ^ 2\right)$

= $\ln \left(\frac{3}{1024}\right)$