Enter a problem...

# Precalculus Examples

Step 1

Interchange the variables.

Step 2

Rewrite the equation as .

Subtract from both sides of the equation.

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

Expand by moving outside the logarithm.

Divide each term in by and simplify.

Divide each term in by .

Simplify the left side.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Step 3

Replace with to show the final answer.

Step 4

To verify the inverse, check if and .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Combine the opposite terms in .

Subtract from .

Add and .

Expand by moving outside the logarithm.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Simplify each term.

Use the change of base rule .

Exponentiation and log are inverse functions.

Combine the opposite terms in .

Add and .

Add and .

Since and , then is the inverse of .