How it works
Compute the logarithm of a value in any base, with the natural and base-10 logarithms shown alongside.
Enter a value and a base. The calculator returns the logarithm of the value in that base and also shows the natural logarithm (ln) and the base-10 logarithm. The value must be positive and the base positive and not equal to 1; invalid inputs get a clear message instead of NaN.
Formula
log_b(x) = ln(x) ÷ ln(b); ln(x) = log base e; log10(x) = log base 10.
x- Value to take the logarithm of (number)
b- Logarithm base (number)
Examples
- Log base 2 of 8Value 8 · base 23
- Log base 10 of 1000Value 1000 · base 103 · ln 6.90775528
Frequently asked questions
Can the base be e?
Yes: enter 2.718281828, or read the natural logarithm (ln) shown for every value.
Why must the base not be 1?
The logarithm to base 1 is undefined because 1 raised to any power is still 1.
How to read the result
The logarithm answers: to what power must the base be raised to get this value?
Limitations
Real logarithms only: the value must be positive and the base positive and not 1. Results are rounded to eight decimals.
Source: Standard logarithm definitions and the base-change formula.