Logarithm Calculator
Free logarithm calculator: log base 10, natural log (ln), log base 2 or any base, with all three common logarithms of the number at once.
What it does
The logarithm answers the question "to what power must I raise the base to get this number?": log₁₀ 1000 = 3 because 10³ = 1000. This calculator finds the logarithm in base 10, base e (the natural logarithm, ln), base 2 or any other base, using the change-of-base rule, and shows the three common logarithms of the number at once.
How to use it
- Type a positive number.
- Choose the base: 10, e, 2 or another one.
- See the logarithm and the natural, decimal and binary logarithms.
The arithmetic runs in your browser. Nothing you type is sent anywhere and nothing is stored, so you can use these with real numbers.
Frequently asked questions
What is the change-of-base rule?
log_b(x) = ln(x) ÷ ln(b), or log(x) ÷ log(b) with any common base. It lets you calculate a logarithm in any base with a calculator that only has ln or log.
What is the natural logarithm?
The logarithm in base e ≈ 2.71828, written ln. It appears in continuous growth and decay, such as compound interest and radioactive decay.
Why can't I take the log of zero or a negative number?
A positive base raised to any real power is always positive, so no exponent gives zero or a negative number. The base itself must be positive and different from 1.
What are the main properties of logarithms?
The log of a product is the sum of the logs, the log of a quotient is the difference, and the log of a power is the exponent times the log: log(xⁿ) = n·log(x).
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