How do you simplify lne^4?

Feb 22, 2016

$4$
You may put any power in the argument before the $\ln$:
$\ln {e}^{4} = 4 \ln e$ (this goes for $\log$'s to any base)
Then since $e$ is the base of the $\ln$-function ($\ln x = {\log}_{e} x$), it follows that: $\ln e = {\log}_{e} e = 1$, just as ${\log}_{10} 10 = 1$
So: $\ln {e}^{4} = 4 \cdot \ln e = 4 \cdot 1 = 4$