# Find the Inverse y=4^(2x+9)

Interchange the variables.
Solve for .
Rewrite the equation as .
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Expand by moving outside the logarithm.
Apply the distributive property.
Move all the terms containing a logarithm to the left side of the equation.
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Simplify .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
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 .
Simplify terms.
Simplify each term.
Expand by moving outside the logarithm.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Simplify the numerator.