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

Sep 20, 2016

=$\ln \left(\frac{3}{12} ^ 2\right) = \ln \left(\frac{1}{48}\right)$

#### Explanation:

"If you are subtracting logs, then you are dividing the numbers"

$\ln 3 - 2 \ln \left(9 + 3\right)$

=$\ln 3 - \ln {\left(9 + 3\right)}^{2} \text{ } \leftarrow$ using the power law of logs

=$\ln \left(\frac{3}{9 + 3} ^ 2\right)$

=$\ln \left(\frac{3}{12} ^ 2\right) \text{ } \leftarrow$ 2 log terms have become one log term

We can now simplify further:

=$\ln \left(\frac{3}{144}\right)$

=$\ln \left(\frac{1}{48}\right)$