Logarithm Calculator
Compute logarithms in any base, including natural log and log base 10.
What the Logarithm Calculator does
A logarithm answers the question "what power do I raise this base to in order to get x?" Logs turn multiplication into addition, which is why they underpin decibels, pH, earthquake magnitude and compound growth.
Formula
log_b(x) = y ⟺ bʸ = xChange of base: log_b(x) = ln(x) ÷ ln(b)
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Number (x) | number | Yes | Must be greater than zero. Accepts more than 0. |
| Base | number | Yes | Use 10 for common log, or 2.718281828 for natural log. |
How to use it
- Enter Number (x) and Base.
- Select Calculate.
Worked example
How many times must you double $1,000 to reach $8,000?
- Number
- 8
- Base
- 2
log₂(8) = 3, so three doublings.
Frequently asked questions
What is the difference between log and ln?
log usually means base 10; ln is base e (≈2.71828). Both are shown above regardless of the base you enter.
Why is log of zero undefined?
No power of a positive base ever produces zero. As x approaches zero the log heads to negative infinity.