Logarithms

Logarithm Calculator

Calculate the logarithm of a value using a custom base.

Valid inputs

The value must be greater than zero. The base must be greater than zero and cannot equal 1.

Example

log base 10 of 1000 equals 3 because 10^3 = 1000. Natural log uses base e and is common in growth, decay and calculus.

Common mistakes

A logarithm asks what exponent is needed, not what multiplication should be done. Also remember that log base 1 is undefined because 1 raised to any power remains 1.

Limitations

This calculator handles positive real values and positive bases except 1. It does not calculate complex logarithms or symbolic algebra steps.

Last reviewed: 2026-05-17

Before relying on this result

Use this calculator together with the formula, assumptions, limitations and examples on the page. If the topic involves health, tax, lending, investment, legal, safety or current-rate decisions, treat the number as an estimate and check the relevant primary source or professional guidance.

Calculator metadata last reviewed: 2026-05-14.