Log calculator

Calculate the logarithm of a number in any base — including common log (base 10) and natural log (base e).

Number (x)

Base

—

Result

Natural log (ln x)—

Common log (log₁₀ x)—

Base-2 log (log₂ x)—

What a logarithm actually asks

A logarithm answers one question: "what power do I need to raise the base to, in order to get this number?" So log base 10 of 100 equals 2, because 10² = 100. Every log calculation is really just an exponent problem written backwards.

The formula this calculator uses

Since browsers only compute natural log directly, every other base is found with the change-of-base formula:

log_b(x) = ln(x) / ln(b) — divide the natural log of x by the natural log of the base.
The input x must be strictly greater than 0 — logarithms of zero or negative numbers are undefined for real numbers.
The base must be positive and not equal to 1, since any power of 1 always equals 1, making the question unanswerable.

Common log bases and where they show up

Base	Name	Typical use
10	Common log	pH scale, decibels, Richter scale
e (≈2.718)	Natural log	Calculus, compound growth, half-life
2	Binary log	Computer science, information theory