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How do you simplify ${ln e}^{2 y}$ $Ln e^(2y)$ ?

1 Answer

Sep 20, 2016

${ln e}^{2 y} = 2 y$ $ln e^(2y)=color(green)(2y)$

Explanation:

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

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

Therefore if ${ln e}^{2 y} = x$ $ln e^(2y) = x$
then
$XXX {log}_{e} e^{2 y} = x$ $color(white)("XXX")log_e e^(2y)=x$
and
$XXX e^{x} = e^{2 y}$ $color(white)("XXX")e^x = e^(2y)$

$\to x = 2 y$ $rarr x=2y$

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