Logarithm Calculator
Calculate logarithms in any base.
The inverse of exponents
A logarithm answers the question: to what power must a base be raised to get a number. It is the inverse of exponentiation. This calculates logarithms in any base, including the common base ten and the natural logarithm.
Enter a number and base to calculate the logarithm.
Why logarithms turn up everywhere
Logarithms are more practical than they first seem because they turn multiplication into addition and compress vast ranges into manageable scales. That compression is why so many real-world scales are logarithmic: earthquake magnitude, sound in decibels, and acidity in pH all use logarithms, so each step represents a tenfold change, letting a small range of numbers span enormous differences. Logarithms also describe anything that grows or decays exponentially, from compound interest to radioactive decay, by turning those curves into straight lines. Understanding a logarithm as simply the exponent needed to reach a number demystifies a concept that intimidates many people but underlies a surprising amount of science and finance.
Logarithm Calculator FAQ
What is a logarithm?
The power a base must be raised to in order to reach a number — the inverse of exponentiation. The log base 10 of 1000 is 3.
Why are logarithmic scales used?
They compress vast ranges — earthquake magnitude, decibels and pH all use logs, so each step is a tenfold change, spanning huge differences in a small range of numbers.
Is anything uploaded?
No. The calculation happens in your browser.