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