About the Log Calculator
A logarithm answers the question: what power must the base be raised to in order to get this number? Enter a base and a number to find log base b of x, and see the natural log (ln), common log (log10) and binary log (log2) of the same number at once. Switch to antilog mode to do the reverse and raise a base to a power. The base can be any positive number except 1, or the letter e for Euler's number. Answers are rounded to 12 significant digits so that results like log10(1000) show a clean 3.
Updated October 2026
How to use the Log Calculator
- 1Choose Logarithm to find a log, or Antilog to raise a base to a power.
- 2Type the base, or e for the natural logarithm.
- 3Enter the number x (for a log) or the power y (for an antilog).
- 4Read the answer and the ln, log10 and log2 values listed under it.
- 5Press Copy result to copy the answer.
Why logarithms matter
Logarithms turn multiplication into addition, which made them the main calculating tool before electronic calculators. Today they measure things that span huge ranges: earthquake magnitude, sound level in decibels, acidity on the pH scale and the information content of data in bits. Each step on these scales is a multiplication of the underlying quantity, so a log scale keeps numbers manageable.
Rules worth remembering
- log(a × b) = log a + log b
- log(a ÷ b) = log a − log b
- log(a^n) = n × log a
- log base b of b is always 1, and log base b of 1 is always 0
- Change of base: log base b of x = ln x ÷ ln b
Choosing a base
Base 10 is common in science and engineering, base 2 in computing and information theory, and base e in calculus and growth models. The calculator accepts any base, so you can also work with unusual ones, such as base 3 for a ternary problem. Type e to use Euler's number precisely rather than a rounded 2.718.
Related tools
The Exponent Calculator reverses a log by raising numbers to powers, and the Square Root Calculator handles fractional powers. The Scientific Notation Converter helps with very large or very small answers, and the Compound Interest Calculator uses logs to find how long money takes to double. The Quadratic Equation Solver is the next step for algebra.
Features
- Logarithm to any positive base except 1
- Natural log, common log and binary log shown together
- Antilog mode for b raised to y
- Accepts e as a base
- Clean answers: floating-point noise is removed
- Clear errors for zero, negative numbers and invalid bases
- Runs in your browser
Frequently asked questions
What is a logarithm?
A logarithm is the power you raise a base to in order to get a number. Since 10 to the power 3 is 1000, the log base 10 of 1000 is 3. Written another way, if b^y = x then log base b of x equals y.
How do I calculate log base 2 or any other base?
Divide the natural log of the number by the natural log of the base: log base b of x = ln x ÷ ln b. The calculator does this for you, so you only need to type the base and the number.
What is the difference between log and ln?
Log usually means the common logarithm with base 10, while ln means the natural logarithm with base e, about 2.71828. Some computer science texts use log for base 2. This tool lists ln, log10 and log2 together, so you can pick the one you need.
What is an antilog?
An antilogarithm undoes a logarithm. If log base 10 of x is 3, the antilog of 3 is 10 to the power 3, which is 1000. Use antilog mode and enter the base and the power.
Why can't I take the log of zero or a negative number?
No real power of a positive base ever gives zero or a negative result, so the real logarithm does not exist for those inputs. The logarithm of a negative number does exist as a complex number, but this calculator handles real numbers only.
Why can't the base be 1?
One raised to any power is still one, so you can never reach another number with base 1. The base must also be above zero. Any other positive base works, including fractions such as 0.5.