Logarithm Calculator

Logarithm of a number in any base, plus ln and log base 10.

Quick answer: Calculate Logarithms online. Free log calculator supporting natural logs (ln), base 10, and custom logarithmic bases.

log₁₀(1,000)3
Natural log (ln)6.907755
Log base 103

computed locally — nothing leaves your browser

Compute the logarithm of a number in any base, with natural log (ln) and log base 10 shown alongside.

How it works

  1. Enter the target number.
  2. Enter the mathematical base (e.g., 10 or 2).
  3. The system evaluates the change-of-base formula to output the log.

Frequently asked questions

What is a logarithm?

The inverse of exponentiation: log base 2 of 8 is 3, because 2^3 = 8.

ln vs log?

ln is the natural log (base e ~ 2.718); log usually means base 10. Both are shown here.

Why must the number be positive?

No real power of a positive base produces zero or a negative number, so their logarithms are undefined in real numbers.

More in Math & Education