# How do you express in terms of ln2 and ln3 given ln sqrt13.5?

Jul 3, 2016

$\ln \sqrt{13.5} = \frac{3}{2} \ln 3 - \frac{1}{2} \ln 2$

#### Explanation:

$\ln \sqrt{13.5} = \ln \sqrt{{3}^{3} / 2}$

$= \frac{1}{2} \ln \left({3}^{3} / 2\right)$

$= \frac{1}{2} \left(\ln {3}^{3} - \ln 2\right)$

$= \frac{1}{2} \left(3 \ln 3 - \ln 2\right)$

$= \frac{3}{2} \ln 3 - \frac{1}{2} \ln 2$