Example 4

Write the inverse of the exponential function using common logarithms. Evaluate any constants in the logarithmic function.
  1. Isolate the exponential term in the function.
  2. Write the logarithmic function.
  3. Simplify the logarithmic function.
  4. Switch the variables and use for .
  5. Rewrite the logarithmic terms for as common logarithmic fractions using the base change rule.
  6. Substitute the common logarithmic fractions into the equation found in step 4 and simplify.
  7. Evaluate the constant terms.
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