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.

Logarithm Calculator

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