# Find the Inverse y = log base 1/3 of x

Interchange the variables.
Solve for .
Rewrite the equation as .
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for
Apply the product rule to .
One to any power is one.
Rewrite the equation as .
Solve for and replace with .
Replace the with to show the final answer.
Set up the composite result function.
Evaluate by substituting in the value of into .
Since , is the inverse of .
Find the Inverse y = log base 1/3 of x