What you provide
What you provide
- Logarithm argument: Positive value whose logarithm is required.
- Logarithm base: Positive base other than 1.
ALGEBRA / CHANGE OF BASE
Logarithm Calculator
Evaluate a logarithm for any valid positive base and compare the natural and common logarithms of the same argument.
- 01 Calculated in this tab
- 02 Values stay in this browser tab
- 03 Use boundary
Use boundary
Calculation path
The change-of-base identity divides the argument’s natural log by the base’s natural log.
Calculation path
log base b of x = ln(x) / ln(b).
What you receive
What you receive
- Requested logarithm value
- Natural and common logarithms
- Exponentiation check
Use boundary
Choose the maximum decimal places shown. This does not increase source accuracy.
Real logarithms require a positive argument and positive base other than one; complex logarithms are outside this tool.
Results are educational math aids. Check notation, units, rounding, assumptions, and required precision before using an answer in graded, engineering, financial, or safety-critical work.