Logarithm Calculator
Calculate the logarithm of a number for any base.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter a value and base to calculate the logarithm.
Your result
3
Result
AI explanation
Formula
log_base(value) = ln(value) ÷ ln(base)Worked example
log base 10 of 1000
| Field | Value |
|---|---|
| Value | 1000 |
| Base | 10 |
| Result | 3 |
Assumptions
- Both value and base must be positive, and base cannot be 1 (logarithms are undefined in those cases).
Frequently asked questions
What does log base 10 of 1000 equal?
3 — because 10³ = 1000.
What is a common base to use?
Base 10 (common logarithm) and base e ≈ 2.71828 (natural logarithm) are the most common — see the Natural Log Calculator for base e specifically.
Why can't the base be 1?
Any power of 1 equals 1, so log base 1 can't represent any other value — the logarithm is undefined for that base.