Math

Logarithm Calculator

log base 10, natural log and any custom base.

Enter your values

Results update instantly as you type — no submit needed.

Results
log base 10
3
Natural log (ln)
6.90775528
log base 10
3
log base 2
9.96578428

Working

  1. 1log_10(1000) = ln 1000 ÷ ln 10 = 3

Quick answer

A logarithm answers 'what power of the base gives this number?' — log_b(x) = ln(x) ÷ ln(b).

log_b(x) = ln x ÷ ln b

How to use the Logarithm Calculator

  1. 1Enter the number.
  2. 2Enter the base you want.
  3. 3Read the log in your base and the common alternatives.

Frequently asked questions

What is the natural log?

The logarithm to base e (2.71828…), which appears wherever continuous growth or decay is modelled.

Why can't you log a negative number?

No real power of a positive base produces a negative result, so real logs are only defined for positive inputs.