Why Use This Tool?
A logarithm answers 'what power raises the base to get this number' — and every field uses a different default base: 10 for engineering and pH, e for science and finance, 2 for computing. This calculator computes any base and shows the three common ones alongside.
The change-of-base formula (log of any base) is handled internally, so one input serves all four results.
How It Works
- Enter a positive number.
- Set the base — 10 for common log, 2.718… for natural log, 2 for binary.
- Read your base's result plus ln, log10 and log2 for reference.
Frequently Asked Questions
How do I calculate a logarithm in any base?
Divide the natural log of the number by the natural log of the base — the change-of-base formula. The tool applies it for any base you enter.
What is a natural log (ln)?
A logarithm with base e (≈2.71828) — the base that makes calculus clean. It appears constantly in growth, decay, and finance calculations.
Why can't I take the log of zero or a negative number?
No power of a positive base produces zero or a negative result, so those inputs are mathematically undefined.
Tips & Things to Watch
- log₂ answers 'how many times can I halve this' — core to algorithms and binary search.
- log of 1 in any base is 0; log of the base itself is 1.
- Doubling time and half-life problems are log base 2 in disguise.