Use the definition of logarithms to translate among logarithms in any base.
Solve an exponential equation exactly by rewriting it in logarithmic form
Problem
What is the solution to the exponential equation \(3^x=20\)?
Big Picture
What this problem is really about
An exponential equation with no convenient common base can still name its unknown exponent exactly. Rewrite that exponent as a logarithm with the original base, then apply change of base so the target's logarithm is divided by the base's logarithm. Substitution with the exact quotient verifies the orientation.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
