Logarithm calculator

Calculate logarithms: log base 10, natural log (ln), log base 2, and any base. Properties, change of base, and condensing/expanding.

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Logarithm basics

logₐ(x) = y means aʸ = x. The logarithm answers: "what power of a gives x?"

Common logarithms

log = log₁₀ (common). ln = logₑ (natural). log(100) = 2 because 10² = 100. ln(e) = 1.

Log laws

log(ab) = log(a) + log(b). log(a/b) = log(a) − log(b). log(aⁿ) = n·log(a). logₐ(a) = 1. logₐ(1) = 0.

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