# Exponential to Logarithmic Form

Exponential functions are inverses of logarithmic functions.

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

Remember a logarithm is an exponent !

Example 1:

Write ${2}^{3}=8$ in logarithmic form.

${\mathrm{log}}_{2}8=3$

Example 2:

Write ${c}^{a}=d$ in logarithmic form.

${\mathrm{log}}_{c}d=a$