log Logarithm Calculator
Compute logarithms in any base — log base 10, natural log (ln), log base 2, or a custom base. Also find antilogarithms and apply the change-of-base formula.
Logarithm
Antilogarithm
Enter a log value to find the original number (base^value).
Logarithm Formulas
Worked Examples
Example — log₅(125)
Example — Antilog of 3
Frequently Asked Questions
A logarithm answers the question: to what exponent must we raise the base to get a given number? If logₐ(x) = y, then aʸ = x. Logarithms are the inverse of exponentiation.
log (common logarithm) uses base 10, while ln (natural logarithm) uses base e ≈ 2.71828. ln appears naturally in calculus, growth/decay models, and statistics, while log base 10 is common in chemistry (pH) and engineering (decibels).
The change-of-base formula allows computing logₐ(x) using any other base: logₐ(x) = log(x)/log(a) = ln(x)/ln(a). This is how calculators compute logarithms in arbitrary bases.
The antilogarithm is the inverse of the logarithm. If log(x) = y, then the antilog of y is x = 10ʸ. For natural logs, the antilog of y is eʸ. Antilogs are used to reverse logarithmic transformations.
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