# How do you solve e^x=2?

Sep 4, 2016

$x = \ln 2$

#### Explanation:

Make use of the $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\log {x}^{n} = n \log x} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Using this law allows us to obtain x as a multiplier

First step - take ln of both sides.

$\Rightarrow \ln {e}^{x} = \ln 2 \Rightarrow x {\cancel{\ln e}}^{1} = \ln 2 \Rightarrow x = \ln 2$