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Logarithm Calculator

Find the logarithm of a number in any base, with ln and log₁₀ shown too.
Must be greater than 0.
Positive and not equal to 1.
logₓ(x)
3
ln(x)

6.907755

log₁₀(x)

3

Formula
logₐ(x) = ln(x) ÷ ln(b)

About this calculator

A logarithm answers the question: to what power must the base be raised to produce a given value? For example, log₁₀(1000) = 3 because 10³ = 1000. The natural log uses base e (≈ 2.71828) and the common log uses base 10.

This calculator uses the change-of-base formula, logₐ(x) = ln(x) / ln(b), which lets it compute a logarithm in any base from the natural logarithm. Logarithms require a positive argument and a positive base other than 1.

Frequently asked questions

ln is the natural logarithm with base e (≈ 2.718), while "log" usually means the common logarithm with base 10. Both are special cases of the general logarithm.

Logarithms are only defined for positive arguments because no real power of a positive base produces zero or a negative number.

It lets you compute a logarithm in any base using another base: logₐ(x) = log_c(x) / log_c(b). This calculator uses the natural log as base c.

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