Skip to content

Log Calculator

Find the logarithm of a number to base 10, base e, base 2 or any base you choose, or work backwards with an antilog, using the change-of-base formula.

Formulas last reviewed: September 2026

Disclaimer: Results are calculated with standard formulas and are meant for learning and quick checks. Please double-check important work, especially anything used for exams, engineering, finance or safety.

Logarithms as the reverse of powers

A logarithm answers the question: what power must I raise the base to, to get this number? Because 10³ = 1,000, the log base 10 of 1,000 is 3. Logs turn multiplication into addition and are used for pH, decibels, earthquake magnitudes, compound growth and more.

This calculator finds logs to base 10, base e (the natural log, ln), base 2 or any base you choose. It can also work backwards with an antilog.

How it is calculated

log_b(x) = ln(x) ÷ ln(b)
Antilog: b^y

Worked example

Three logs

log₁₀(1000)
3
log₂(8)
3
ln(e²)
2
log₅(125)
3

Useful log rules

  • log(a × b) = log a + log b
  • log(a ÷ b) = log a − log b
  • log(a^n) = n × log a
  • The log of 1 is always 0, and the log of the base itself is always 1.

Frequently asked questions

What is the difference between log and ln?

Log usually means base 10, while ln is the natural logarithm with base e (about 2.71828). They are related by a constant factor.

Why can't I take the log of zero or a negative number?

No real power of a positive base gives zero or a negative result, so the logarithm of those numbers is not defined for real numbers.

What is an antilog?

It is the inverse of a log: raise the base to that value. The antilog of 3 to base 10 is 1,000.

How do I calculate a log to a base my calculator lacks?

Use the change-of-base formula: divide the natural log of the number by the natural log of the base. This calculator does that for you.