Algebra Examples

Find the Inverse f(x) = log base 4 of x
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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Rewrite the equation as .
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Rewrite the equation as .
Step 4
Replace with to show the final answer.
Step 5
Verify if is the inverse of .
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To verify the inverse, check if and .
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Exponentiation and log are inverse functions.
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Use logarithm rules to move out of the exponent.
Logarithm base of is .
Multiply by .
Since and , then is the inverse of .
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