A logarithm is the inverse operation of exponentiation, answering "to what power must a base be raised to produce a given number?"
If bΛ£ = y, then log_b(y) = x. Common bases are 10 (common log) and e β 2.718 (natural log, ln). Key properties: log(ab) = log a + log b, log(a/b) = log a - log b, log(aβΏ) = n log a. Logarithms convert multiplication to addition, making complex calculations simpler. They are used in pH scales, earthquake magnitude (Richter), sound (decibels), population growth, and computer science (algorithm complexity).
Logarithms were invented by John Napier in 1614 to simplify astronomical calculations. Henry Briggs collaborated with Napier to develop base-10 logarithms. The natural logarithm base e was studied by Leonhard Euler in the 18th century. Slide rules, based on logarithms, were essential calculation tools until electronic calculators became widespread in the 1970s.