How to use the Logarithm Calculator
- Choose log or antilog.
- Pick a base — 10, e, 2 or your own.
- Enter the number and read the result.
What does this tool do?
A logarithm answers the question “what power do I raise the base to, to get this number?”. log₁₀(1000) = 3 because 10³ = 1000. Natural logs use the base e ≈ 2.71828 and appear throughout growth, decay and calculus.
Any base can be calculated with the change-of-base rule log_b(x) = ln(x) ÷ ln(b). The calculator shows ln, log₁₀ and log₂ alongside your chosen base.
Why use it?
- Any base, not just 10 and e.
- Antilog mode for the reverse.
- Change-of-base working shown.
The formula
log_b(x) = ln(x) ÷ ln(b)
antilog_b(y) = bʸ
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Frequently asked questions
Why can't I take the log of a negative number?
No real power of a positive base gives a negative result, so logarithms are only defined for positive numbers.
Last reviewed by the M2Toolkit team.