How do you simplify Ln e^(2y)?

Sep 20, 2016

$\ln {e}^{2 y} = \textcolor{g r e e n}{2 y}$

Explanation:

$\ln$ is equivalent to ${\log}_{e}$

${\log}_{b} a = c \Leftrightarrow {b}^{c} = a$

Therefore if $\ln {e}^{2 y} = x$
then
$\textcolor{w h i t e}{\text{XXX}} {\log}_{e} {e}^{2 y} = x$
and
$\textcolor{w h i t e}{\text{XXX}} {e}^{x} = {e}^{2 y}$

$\rightarrow x = 2 y$