Logarithm Calculator

Logarithm Calculator computes logarithms in any base, common log (base 10), natural log (ln, base e), log base 2, or a custom base, for maths, science, and engineering.

At heart, a logarithm answers a simple question: what power must you raise the base to in order to reach a given number? log₁₀(1000) = 3 because 10³ = 1000. That makes it the inverse of exponentiation, and the natural tool for anything involving exponential growth, decay, or enormous ranges of scale.

The common bases each have their home: base 10 for general use, natural log (base e) at the heart of calculus and growth/decay processes, and base 2 throughout computer science and information theory. Picking the base your problem uses is the main decision; the calculator handles the arithmetic.

Logs also explain why scales like decibels and the Richter scale are logarithmic, they compress vast ranges so each step multiplies rather than adds (a magnitude-6 quake releases ~32× the energy of a magnitude-5). The calculation runs in your browser with nothing uploaded. Pair it with the Permutation-Combination and other ToolsMonk STEM tools.