Logarithm Calculator
Calculate the logarithm of a number in any base, plus the natural log.
Logarithm
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Natural log (ln)
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Common log (base 10)
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Check
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Results update as you type.
About this calculator
A logarithm answers the question "what power do I raise the base to, to get this number?" This calculator computes the log in any base you choose (default base 10) and also shows the natural log (base e). It uses the change-of-base rule: log_b(x) = ln(x) / ln(b).
Frequently asked questions
What is a logarithm?
It is the inverse of exponentiation. log₁₀(1000) = 3 because 10³ = 1000. The log tells you the exponent needed to reach a number.
What is the change-of-base formula?
To find a log in any base from a calculator that only has ln or log₁₀, use log_b(x) = ln(x) / ln(b).
Results are estimates for general guidance only, not financial, medical or tax advice.