Logarithms Explained

This log calculator evaluates log_b(x) for any positive base. A logarithm is the inverse of exponentiation: log_b(x) is the exponent to which b must be raised to produce x. Change of base converts everything through natural logs.

Common, Natural, and Binary

Base 10 (common log) measures orders of magnitude, base e (natural log) arises in growth and decay, and base 2 (binary log) counts doublings — central to computing and information theory. All three are shown alongside your custom base.

Verification

Every result is checked by re-exponentiating: b^log_b(x) must reproduce x. If the displayed value and the inverse check disagree, you would know immediately — with double precision they agree to six decimals.