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Calculators / Math / Logarithm
Logarithm calculator
Calculate natural and base-10 logarithms of a positive number.
On this page
Natural logarithm6.91
Base-10 logarithm3
Logarithm in selected base3
Calculator controls
How to calculate
Calculate natural and base-10 logarithms of a positive number.
log base b of x = ln(x) ÷ ln(b), where x > 0, b > 0 and b ≠ 1.
Worked example
Positive number: 1000; Logarithm base (positive, not 1): 10.
Natural logarithm: 6.91 ; Base-10 logarithm: 3 ; Logarithm in selected base: 3 .
Assumptions and limits
Logarithms are defined here only for positive real values.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate natural and base-10 logarithms of a positive number. The displayed figures use the inputs and formula shown on this page.
When this tool is useful
Use the logarithm to compare a scenario, check an estimate, or verify a manual calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Positive number | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Logarithm base (positive, not 1) | Enter a number of at least 1e-12 and no more than 1000000000000. |
Frequently asked questions
What should I check before using the logarithm result?
Logarithms are defined here only for positive real values.
Is this logarithm result exact?
It is exact for the stated mathematical model and entered values. Real-world results can differ when rates, timing, fees, definitions or measurement conditions differ.