Logarithm Calculator

Compute logs in any base — 2, e, 10 or custom. Calculate logarithms in base 2, natural log (base e), base 10 or any custom base. Handles decimals and shows the exact expression. Free log calculator.

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Acerca de Logarithm Calculator

Logarithms answer "what power turns the base into this number?" — the reverse of exponentiation and the backbone of pH values, decibels, earthquake magnitudes, algorithm complexity and compound growth. Enter a number and choose base 2, e (natural log), 10 (common log) or a custom base; the calculator returns the result to high precision and shows which expression it evaluated, so you can verify it against a textbook answer.

Cómo usar Logarithm Calculator

  1. Enter the number (must be positive).
  2. Choose the logarithm base.
  3. Read the result and the expression shown.
  4. Switch bases to compare values.

Características principales

Why can’t I take the log of zero or a negative number?
No real power of a positive base ever produces zero or a negative result, so those logarithms are undefined over the real numbers.
What is the change-of-base rule?
log in any base b equals log(x) ÷ log(b) using any other base — the identity this calculator uses for custom bases.

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