# Find the Inverse y=e^(3x+1) 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 the left side.
Expand by moving outside the logarithm.
The natural logarithm of is .
Multiply by .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Split the fraction into two fractions.
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 each term.
Rewrite as .
Simplify by moving inside the logarithm.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Apply the distributive property.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Use logarithm rules to move out of the exponent.
The natural logarithm of is .
Multiply by .
Combine the opposite terms in .
Combine the numerators over the common denominator.
Subtract from .
Divide by .