Logarithm Calculator
Last updated: November 5, 2026
Calculate a logarithm with an editable base plus natural and base-10 logarithms.
Logarithm with selected base
—
- Natural logarithm ln(x): —
- Base-10 logarithm log₁₀(x): —
- Base raised to the result: —
On this page
Quick summary: Calculate a logarithm with an editable base plus natural and base-10 logarithms.
Read the complete guide
Updated reference sections in this guide are in English.
What this calculator estimates
Calculate a logarithm with an editable base plus natural and base-10 logarithms.
How to use it
Enter Positive number; Logarithm base. Select Calculate to update the results.
How the calculation works
A logarithm with base b is calculated as the natural logarithm of x divided by the natural logarithm of b.
Worked example: starting scenario
| Positive number | 1000 |
|---|---|
| Logarithm base | 10 |
| Logarithm with selected base | 3 |
|---|---|
| Natural logarithm ln(x) | 6.907755278982 |
| Base-10 logarithm log₁₀(x) | 3 |
| Base raised to the result | 1,000 |
Important limitations
The number and base must be positive, and the base cannot equal one.
A logarithm asks for an exponent
log₂(8) = 3 because 2³ = 8. A base between zero and one is valid: log₀.₅(8) = −3. The input number must be positive, and the base must be positive and different from 1. Natural logarithm uses base e, while the separate common-log output uses base 10. Reconstructing base raised to the result is a rounding check, not an independent measurement.