Logarithm calculator
Find the logarithm of a positive value in any positive base other than one. Calculate common, binary and custom-base logarithms.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Positive value | Enter positive value using the definition in the method and example. |
| Logarithm base | Enter logarithm base using the definition in the method and example. |
Understanding your result
Read Logarithm in the units and model stated on this page. The formula log_b(x) = ln(x) ÷ ln(b) defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Using a different mathematical definition or operation than the one stated by this tool.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
What exponent turns this base into this number?
Enter a positive value and a positive base other than one. The logarithm answers which exponent gives that value from the base.
Common uses
- Find an exponent when the base and resulting value are known.
- Calculate common, binary or custom-base logarithms.
How it works
The logarithm answers which exponent turns the base into the value. Change of base divides the natural logarithm of the value by the natural logarithm of the base. The value and base must be positive, and base 1 is undefined.
Worked example
log₂(1,024) = 10 because 2¹⁰ = 1,024. log₁₀(1,000) = 3.