Logarithm Calculator
Calculate a logarithm in any base, plus natural (ln), common (log₁₀) and binary (log₂) logs.
How to use it
- Enter the value The positive number x to take the log of.
- Enter the base Any positive base other than 1.
- Read the results Your custom base plus ln, log₁₀ and log₂.
Examples
| log₂(8) | 3 |
|---|---|
| log₁₀(1000) | 3 |
About this tool
A logarithm answers the question “what power must I raise the base to, to get this number?” This calculator computes the log of any positive value in a base you choose, and at the same time shows the three most common logarithms.
Seeing the natural, common and binary logs together is handy across science, engineering and computing, where each base crops up in different contexts. The custom base covers everything else. All the maths runs locally in your browser.
Frequently asked questions
What's the difference between the logs?
They differ only by base — ln uses e, the common log uses 10, and the binary log uses 2. The custom base lets you use any value you like.
Why must x be positive?
Logarithms are only defined for positive numbers, so the tool asks for a value greater than zero.
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Updated June 14, 2026