Find the Inverse 13+ log of x

Rewrite the equation as ${\displaystyle 13+\log \left(y\right)=x}$.

Subtract ${\displaystyle 13}$ from both sides of the equation.

Rewrite ${\displaystyle \log \left(y\right)=x-13}$ 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 ${\displaystyle y={10}^{x-13}}$.

To verify the inverse, check if ${\displaystyle f^{-1}\left(f\left(x\right)\right)=x}$ and ${\displaystyle f\left(f^{-1}\left(x\right)\right)=x}$.

Evaluate ${\displaystyle f^{-1}\left(f\left(x\right)\right)}$.

Evaluate ${\displaystyle f\left(f^{-1}\left(x\right)\right)}$.

Since ${\displaystyle f^{-1}\left(f\left(x\right)\right)=x}$ and ${\displaystyle f\left(f^{-1}\left(x\right)\right)=x}$, then ${\displaystyle f^{-1}\left(x\right)={10}^{x-13}}$ is the inverse of ${\displaystyle f\left(x\right)=13+\log \left(x\right)}$.