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# Precalculus Examples

Interchange the variables.

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.

Replace with to show the final answer.

To verify the inverse, check if and .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Simplify each term.

Use logarithm rules to move out of the exponent.

The natural logarithm of is .

Multiply by .

Combine the opposite terms in .

Subtract from .

Add and .

Evaluate .

Set up the composite result function.

Evaluate by substituting in the value of into .

Combine the opposite terms in .

Add and .

Add and .

Exponentiation and log are inverse functions.

Since and , then is the inverse of .