🪵 Log Calculator
A logarithm answers the question “how many times must I multiply the base by itself to get this number?” Since 10³ = 1000, log₁₀(1000) = 3. Logs turn multiplication into addition, which is why they power everything from earthquake scales to compound interest.
Enter the number and pick the base: 10 for common logs, e for the natural log, 2 for computing, or type any custom base. The number must be positive and the base must be positive and not 1.
How to use this calculator
Type the number, choose the logarithm base, and press Calculate.
- Type a positive number into the Number field.
- Pick the Base: 10 for the common log, e for the natural log, 2 for computing, or Custom.
- If you chose Custom, type your own base into the Custom base field.
- Press Calculate and read the logarithm as the headline result.
Frequently asked questions
What is a logarithm?
A logarithm answers how many times you multiply the base by itself to reach the number. Since 10 x 10 x 10 = 1000, log base 10 of 1000 equals 3.
What are the common logarithm bases?
Base 10 is the common log used in science and engineering, base e (about 2.718) is the natural log used in calculus and growth models, and base 2 is used in computing and information theory.
Why must the number be positive?
No power of a positive base can produce zero or a negative number, so logarithms are only defined for positive numbers. The base itself must also be positive and different from 1.
Can you show a worked example?
Log base 2 of 8 equals 3, because 2 x 2 x 2 = 8. Try it: enter 8, choose base 2, and the calculator returns 3.