A logarithm answers “to what power must the base be raised to get this number?” It turns multiplication into addition.
How to use the Log Calculator
- Number
- Base
- Want to work backwards? Type a value into log_b(x) and Number is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
The change-of-base formula divides the natural log of x by the natural log of the base.
Inputs explained
| Field | What to enter |
|---|---|
| Number | A number |
| Base | A number |
What each result means
- log_b(x) = [Natural log ln(x)]([Number]) ÷ [Natural log ln(x)]([Base])
- Natural log ln(x) = [Natural log ln(x)]([Number])
- log₁₀(x) = log10([Number])
- log₂(x) = [Natural log ln(x)]([Number])÷[Natural log ln(x)](2)
Example values
How the main result changes when Number changes and everything else stays at the example values above:
| Number | log_b(x) |
|---|---|
| 500 | 2.699 |
| 750 | 2.8751 |
| 1,000 | 3 |
| 1,250 | 3.0969 |
| 1,500 | 3.1761 |
| 2,000 | 3.301 |
Formula
log_b(x) = ln(x) ÷ ln(b)Worked example
Inputs — Number: 1,000; Base: 10.
Results — log_b(x) = 3; Natural log ln(x) = 6.90775528; log₁₀(x) = 3; log₂(x) = 9.96578428.
Key terms
- Natural log
- Logarithm with base e ≈ 2.71828.
Frequently asked questions
What is the log of a negative number?
Not defined among real numbers.
What is an antilog?
The inverse: if log_b(x) = y, then x = b^y.
What formula does the Log Calculator use?
log_b(x) = ln(x) ÷ ln(b).
Can I work backwards from the result?
Yes. Type the result you want into log_b(x) and the calculator finds the matching number.