Logarithm Calculator
Compute logarithms in any base — with step-by-step solution.
About this calculator
Calculates logarithms in any base. Uses the change-of-base formula: log_b(x) = ln(x) / ln(b). For negative values, the calculator shows 'undefined' since real logarithms require positive arguments.
How logarithms work
A logarithm answers the question: to what power must the base be raised to produce the given value? If b^y = x, then log_b(x) = y. The three most common bases are 10 (common log), e (natural log, ln), and 2 (binary log). Logarithms turn multiplication into addition and are fundamental to information theory, signal processing, pH chemistry, and earthquake magnitudes.