Logarithm Calculator
Enter a number and a base to calculate the logarithm. The natural log and the base 10 and base 2 logs are shown too.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- log base b of x = ln(x) ÷ ln(b)
- ln is the natural log, to base e
- log₁₀ and log₂ use base 10 and base 2
- Results are rounded to 12 significant digits and shown to 6 decimal places
To go the other way, use the exponent calculator. For compound growth over time, use the compound interest calculator.
Worked example
- log₁₀(1,000) = 3, because 10³ = 1,000
- log₂(8) = 3, because 2³ = 8
- ln(1,000) = 6.907755
Why your number may differ
Computers work with limited precision, so a result that should be exact may differ in the last digits, which is why the value is rounded.
Frequently asked questions
What is a logarithm?
The logarithm log base b of x is the power you must raise b to in order to get x. Since 10³ = 1,000, log₁₀(1,000) = 3.
What is the natural log?
ln(x) is the logarithm to base e, where e is about 2.71828. It appears in growth, decay and compound interest.
Why must x be above 0?
No power of a positive base gives zero or a negative number, so the logarithm of 0 or a negative number is not a real number.