# Logarithmic to Exponential Form

Logarithmic functions are inverses of exponential functions .  So, a log is an exponent !

$y={\mathrm{log}}_{b}x$ if and only if ${b}^{y}=x$ for all $x>0$ and $0 .

Example 1:

Write ${\mathrm{log}}_{5}125=3$ in exponential form.

${5}^{3}=125$

Example 2:

Write ${\mathrm{log}}_{z}w=t$ in exponential form.

${z}^{t}=w$