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Algebra Examples
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 3.3
Expand the left side.
Step 3.3.1
Expand by moving outside the logarithm.
Step 3.3.2
The natural logarithm of is .
Step 3.3.3
Multiply by .
Step 4
Replace with to show the final answer.
Step 5
Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
Step 5.2.1
Set up the composite result function.
Step 5.2.2
Evaluate by substituting in the value of into .
Step 5.2.3
Use logarithm rules to move out of the exponent.
Step 5.2.4
The natural logarithm of is .
Step 5.2.5
Multiply by .
Step 5.3
Evaluate .
Step 5.3.1
Set up the composite result function.
Step 5.3.2
Evaluate by substituting in the value of into .
Step 5.3.3
Exponentiation and log are inverse functions.
Step 5.4
Since and , then is the inverse of .