# How do you simplify ln(5e^6)?

May 1, 2017

$\ln \left(5 {e}^{6}\right) = \ln \left(5\right) + 6$

#### Explanation:

Note that if $a , b > 0$ then

$\ln \left(a b\right) = \ln \left(a\right) + \ln \left(b\right)$

Also note that for any real value of $x$:

$\ln \left({e}^{x}\right) = x$

So:

$\ln \left(5 {e}^{6}\right) = \ln \left(5\right) + \ln \left({e}^{6}\right) = \ln \left(5\right) + 6$