Use the definition of logarithms to translate among logarithms in any base.
Evaluate an exact logarithm by rewriting it as an exponential equation
Problem
Evaluate this logarithm exactly: \(\log_5(125)\).
Big Picture
What this problem is really about
Exact logarithms are exponent questions, so look for a power relationship before using a calculator. Translate the logarithm into a base-to-an-unknown-power equation and factor the argument into repeated copies of that base. The count of those factors gives the exact exponent immediately.
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