# What is the inverse of a logarithmic function?

${\log}_{b} \left(x\right) = y \implies$ switch x and y:
${\log}_{b} \left(y\right) = x \implies$ solve for y:
${b}^{{\log}_{b} \left(y\right)} = {b}^{x}$
$y = {b}^{x} \implies$ hence: ${\log}_{b} \left(x\right)$ and ${b}^{x}$ are the inverse functions.