# How do you simplify lne^2?

Sep 5, 2016

2

#### Explanation:

The natural log function lnx and the exponential function ${e}^{x}$ are
$\textcolor{b l u e}{\text{inverse functions}}$

That is $f \left(x\right) = {e}^{x} \text{ then} {f}^{-} 1 x = \ln x$ and in general

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{f}^{-} 1 \left(f \left(x\right)\right) = x} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \ln {e}^{2} = 2$