Logarithm Calculator
Compute logarithms in any base — log₁₀, ln, log₂, or any custom base, with the full working via the change-of-base formula.
Quick base
Fill in base and value.
About this calculator
Calculates logarithms in any base. Uses the change-of-base formula: log_b(x) = ln(x) / ln(b). For non-positive values, the result is 'undefined' since real logarithms require positive arguments.
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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.