Logarithm Calculator
log base 10, natural log and any custom base.
Enter your values
ⓘ Live results
Results
- log base 10
- 3
- Natural log (ln)
- 6.90775528
- log base 10
- 3
- log base 2
- 9.96578428
Working
- 1log_10(1000) = ln 1000 ÷ ln 10 = 3
Quick answer
A logarithm answers 'what power of the base gives this number?' — log_b(x) = ln(x) ÷ ln(b).
log_b(x) = ln x ÷ ln b
How to use the Logarithm Calculator
- 1Enter the number.
- 2Enter the base you want.
- 3Read the log in your base and the common alternatives.
Worked example
Using the values the calculator loads with:
Inputs
- Number1000
- Base10
Results
- log base 103
- Natural log (ln)6.90775528
- log base 103
- log base 29.96578428
- log_10(1000) = ln 1000 ÷ ln 10 = 3
Frequently asked questions
What is the natural log?
The logarithm to base e (2.71828…), which appears wherever continuous growth or decay is modelled.
Why can't you log a negative number?
No real power of a positive base produces a negative result, so real logs are only defined for positive inputs.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.