📐 Logarithm Calculator
Calculate logarithms with any base, plus natural log (ln) and log base 10.
Understanding Logarithms
A logarithm answers the question: to what power must the base be raised to produce a given number? For example, log₁₀(100) = 2 because 10² = 100. Common bases are 10 (common log), e ≈ 2.718 (natural log), and 2 (binary log).
Logarithm Properties
Key properties: log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b), log(aⁿ) = n·log(a). The change of base formula is log_b(x) = ln(x) / ln(b). Logarithms are used in science, engineering, music, and data analysis.
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