Logarithm Calculator
Calculate common (base 10), natural (base e), binary (base 2), or any custom base logarithm. Includes antilog and change-of-base formula.
Logarithm Reference
What Is a Logarithm?
logₐ(x) asks: 'a to what power equals x?' log₁₀(1000) = 3 because 10³ = 1000. ln(e²) = 2 because e² = e². Logarithms are the inverse of exponentials.
Change of Base Formula
logₐ(x) = log(x) / log(a) = ln(x) / ln(a). Any base can be computed using log₁₀ or ln on a calculator. Example: log₂(32) = log(32)/log(2) = 1.50515/0.30103 = 5.
Logarithm Laws
Product: log(ab) = log(a) + log(b). Quotient: log(a/b) = log(a) − log(b). Power: log(aⁿ) = n·log(a). These rules convert multiplication into addition — the original purpose of logarithm tables before calculators.
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