Solve the Inequality for x natural log of x>=3

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

Rewrite ${\displaystyle \ln \left(x\right)=3}$ 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 ${\displaystyle x=e^3}$.

Set the argument in ${\displaystyle \ln \left(x\right)}$ greater than ${\displaystyle 0}$ to find where the expression is defined.

The domain is all values of ${\displaystyle x}$ that make the expression defined.