Replace with .

Interchange the variables.

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

Rewrite the equation as .

Add to both sides of the equation.

Replace the with to show the final answer.

Set up the composite result function.

Evaluate by substituting in the value of into .

Exponentiation and log are inverse functions.

Combine the opposite terms in .

Add and .

Add and .

Since , is the inverse of .

Find the Inverse f(x) = log base 6 of x-2