math

Logarithm

The inverse of exponentiation — the logarithm of a number tells you the exponent needed to produce that number from a given base.

A logarithm answers the question: "What power must I raise the base to, to get this number?" If b^x = y, then log_b(y) = x.

Common Bases

  • log₁₀ (common log): Used in pH, decibels, Richter scale
  • ln (natural log, base e ≈ 2.718): Used in calculus, finance, growth models
  • log₂ (binary log): Used in computer science, information theory

Key Properties

log(a×b) = log(a) + log(b) | log(a/b) = log(a) − log(b) | log(a^n) = n·log(a)

Related Calculators

Related Terms