What this calculator does
This tool finds the logarithm of a positive number to any positive base you choose, such as base 10 (common log) or base e (natural log, about 2.71828). It also shows the natural log and base-10 log for reference.
The formula used
A logarithm answers the question "to what power must the base be raised to get this number?" Since most calculators only have natural log built in, this tool uses the change-of-base formula: logb(x) = ln(x) ÷ ln(b), where ln is the natural logarithm.
Good to know
Logarithms are only defined for positive numbers, and the base must be positive and not equal to 1. If an invalid number or base is entered, the calculator falls back to a safe default (base 10) rather than showing an error. Intended for general educational and reference use.
Last reviewed August 2026