Solve for x 2 = natural log of x

Rewrite the equation as ${\displaystyle \ln \left(x\right)=2}$.

To solve for ${\displaystyle x}$, rewrite the equation using properties of logarithms.

Rewrite ${\displaystyle \ln \left(x\right)=2}$ in exponential form using the definition of a logarithm. If ${\displaystyle x}$ and ${\displaystyle b}$ are positive real numbers and ${\displaystyle b\ne 1}$, then ${\displaystyle {\log }_b\left(x\right)=y}$ is equivalent to ${\displaystyle b^y=x}$.

Rewrite the equation as ${\displaystyle x=e^2}$.