ClarityHow to use this tool
- Enter value, base.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Value | Numeric value. Must be greater than zero. | 1000 |
| Base | Numeric value. Must be greater than zero. | 10 |
Result for these sample inputs
3
- Natural logarithm of value
- 6.90775528
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
log_b(x) = ln(x) ÷ ln(b). This gives the exponent to which b must be raised to produce x.
log₁₀(1,000) = 3 because 10³ = 1,000.
What to keep in mind
The value and base must be positive, and the base cannot be one. This tool calculates real logarithms only.
Common questions
Can a logarithm be negative?
Yes. In a base greater than one, values between zero and one have negative logarithms.
What happens with base one?
One raised to any power remains one, so the usual logarithm is not defined.
Methodology maintained by ClarityKit. How these tools are built and checked.