# How do you solve ln(x)=2?

Mar 30, 2018

$\implies x = {e}^{2}$

#### Explanation:

$\implies \ln \left(x\right) = 2$

Natural log has a base of $e$. More explicitly we can write:

$\implies {\ln}_{e} \left(x\right) = 2$

Logarithms have the following form:

$\implies {\log}_{a} \left(x\right) = b$

They also have the property:

$\implies {a}^{{\log}_{a} \left(x\right)} = x$

So we can raise both sides of our equation by $e$ to extract the $x$:

$\implies {e}^{\ln \left(x\right)} = {e}^{2}$

$\implies x = {e}^{2}$