# How do you condense 2 ln 4 - ln 2?

May 7, 2016

$2 \ln 4 - \ln 2 = \ln 8$

#### Explanation:

As $a \ln b = \ln {b}^{a}$ and $\ln p - \ln q = \ln \left(\frac{p}{q}\right)$

$2 \ln 4 - \ln 2$

= $\ln {4}^{2} - \ln 2$

= $\ln 16 - \ln 2$

= $\ln \left(\frac{16}{2}\right) = \ln 8$