# How do you simplify ln(3sqrte^13 ) ?

Nov 11, 2016

#### Answer:

$= \ln 3 + 6.5$

#### Explanation:

$\ln \left(3 {\sqrt{e}}^{13}\right)$

First expand it by using the log rule: $\ln \left(a b\right) = \ln a + \ln b$

$= \ln 3 + \ln {\sqrt{e}}^{13}$

We can rewrite the second term as $\ln \left({e}^{\frac{13}{2}}\right)$

$= \ln 3 + \ln \left({e}^{\frac{13}{2}}\right)$

$= \ln 3 + \frac{13}{2} \ln e$

$= \ln 3 + 6.5$