log Log Calculator

About this Log Calculator

This log calculator finds the logarithm of any positive number in base 10, base 2, the natural base e, or a custom base you choose. Logarithms are the inverse of powers: log₁₀(1000) = 3 because 10³ = 1000. They are used in science, engineering, sound and earthquake scales, and computing.

How to use it

1. Enter the positive number you want the log of.
2. Pick a base — 10, 2, e, or choose Custom and type your own base.
3. Click Calculate log to see the result, with ln and log₁₀ shown for reference.

Example

log₁₀(100) = 2, because 10² = 100; and the natural log ln(100) ≈ 4.6052.

Frequently asked questions

Why must the number be positive?

No power of a positive base ever gives zero or a negative result, so logs of those numbers have no real answer.

What is the natural log (ln)?

It is the logarithm in base e (≈ 2.71828). It appears in growth, decay and finance formulas, and this tool always shows it for reference.

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