# How do you condense 2ln6 - ln3?

May 24, 2016

$\ln \left(12\right)$

#### Explanation:

Logs are subtracted if the source numbers are divided.

If the source number is raised to a power than you can multiply the loge by the value of that power. Suppose you had $\log \left({x}^{a}\right)$ then this could be written as $a \log \left(x\right)$

So $2 \ln \left(6\right) - \ln \left(3\right) \text{ " ->" " ln(6^2)-ln(3)" " ->" } \ln \left({6}^{2} / 3\right)$

$= \ln \left(12\right)$