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Free Logarithm Calculator

Calculate logarithms in any base — log base 10, natural log (ln), log base 2, and custom bases.

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Formula

log_b(x) = ln(x) / ln(b) — log₁₀(100) = 2 because 10² = 100

Understanding Logarithms

A logarithm is the inverse of exponentiation. If bˣ = y, then log_b(y) = x. For example, since 2³ = 8, log₂(8) = 3.

Common Logarithm Bases

Base 10 (common log): Used in science, decibels, pH scale. Base e (natural log): Used in calculus, growth/decay, finance. Base 2: Used in computing, binary, information theory.

Frequently Asked Questions

What is a logarithm?

A logarithm answers: 'To what power must I raise the base to get this number?' log₁₀(1000) = 3 because 10³ = 1000.

What's the difference between log and ln?

log usually means log base 10 (common logarithm). ln means log base e ≈ 2.718 (natural logarithm). In computer science, log often means log base 2.