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Logarithm Calculator - Log Base 10, Natural Log, Custom Base

Free logarithm calculator. Calculate log base 10, natural log (ln), log base 2, or any custom base logarithm.

Calculate logarithms with any base

Enter your values to see results

and click the "Calculate" button

What is a Logarithm?

A logarithm answers the question: to what power must we raise the base to get a number? For example, log₁₀(100) = 2 because 10² = 100.

log_b(x) = y means b^y = x

Common bases: 10 (common log), e≈2.718 (natural log/ln), 2 (binary log)

What is the difference between log and ln?

Log typically refers to log base 10, while ln (natural log) is log base e (≈2.718). Natural logs are used extensively in calculus and science.

What is log base 2 used for?

Log base 2 (binary logarithm) is used in computer science to measure information in bits and analyze algorithm complexity.

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