How do you simplify ln(e^2lne^3)?

Nov 27, 2016

$= 2 + \ln 3$

Explanation:

Simplifying the expression is determined by applying the
$\text{ }$
following properties:
$\text{ }$
$\textcolor{b l u e}{\ln \left(a \times b\right) = \ln a + \ln b}$
$\text{ }$
$\textcolor{red}{\ln {e}^{a} = a}$
$\text{ }$
$\ln \left({e}^{2} \ln {e}^{3}\right)$
$\text{ }$
$= \ln \left({e}^{2} \times \textcolor{red}{3}\right)$
$\text{ }$
$= \ln \left({e}^{2} \times 3\right)$
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=color(blue)(lne^2 + ln3
$\text{ }$
$= \textcolor{red}{2} + \ln 3$
$\text{ }$