# How do you evaluate lne^(-4x)?

Oct 31, 2016

$- 4 x$

#### Explanation:

$\ln {e}^{- 4 x}$=${\log}_{e} {e}^{- 4 x}$
The way I remember log relationships is
${2}^{3} = 8$ and ${\log}_{2} 8 = 3$ are two ways of writing the same thing.
So if ${\log}_{e} {e}^{- 4 x}$ = n
Then ${e}^{n} = {e}^{- 4 x}$
And $n = - 4 x$

${\log}_{e} {e}^{- 4 x} = - 4 x$
Or $\ln {e}^{- 4 x} = - 4 x$