# How do you condense  ln 3 − 2 ln(9 + 3) ?

Jun 27, 2016

$\ln \left[\frac{1}{48}\right]$

#### Explanation:

Simplify the bracket:

$\ln 3 - 2 \ln \textcolor{b l u e}{\left(9 + 3\right)} = \ln 3 - 2 \ln \textcolor{b l u e}{\left(12\right)}$

If you are subtracting the logs, you must have been dividing the numbers.

Use the power rule first:

$\ln 3 - \textcolor{red}{2} \ln \left(12\right) = \ln 3 - \ln {\left(12\right)}^{\textcolor{red}{2}}$

Write as a log of a single number:

$= \ln \left[\frac{3}{12} ^ 2\right]$

$= \ln \left(\frac{3}{144}\right) = \ln \left[\frac{1}{48}\right]$