Finite Math Examples

Find the Inverse y=9^x
Step 1
Interchange the variables.
Step 2
Solve for .
Tap for more steps...
Step 2.1
Rewrite the equation as .
Step 2.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.3
Expand by moving outside the logarithm.
Step 2.4
Divide each term in by and simplify.
Tap for more steps...
Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
Tap for more steps...
Step 2.4.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
Tap for more steps...
Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
Tap for more steps...
Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Expand by moving outside the logarithm.
Step 4.2.4
Cancel the common factor of .
Tap for more steps...
Step 4.2.4.1
Cancel the common factor.
Step 4.2.4.2
Divide by .
Step 4.3
Evaluate .
Tap for more steps...
Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
Use the change of base rule .
Step 4.3.4
Exponentiation and log are inverse functions.
Step 4.4
Since and , then is the inverse of .