Evaluating Logarithms Step by Step

Pre-Calculus · Axiom Academy

Read a logarithm as a question — "the base to what power gives the argument?" Evaluate . There is nothing to plug into a calculator here — instead we ask the one question every logarithm is really posing: 2 raised to what power gives 32? Every logarithm is an exponent in disguise: the missing power is the answer. Nice work. You evaluated a logarithm with no calculator — just by turning it into a question about exponents. The core question: asks "the base b raised to what power gives a ?" The answer is that exponent. List powers when stuck: writing until you hit the argument turns a logarithm into simple matching. The same question handles every case: Master that one question and you can read any logarithm — no memorizing tables, no calculator.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.