Logarithm calculator (any base)
Pick a base and enter a number to find the power the base must be raised to. Useful in math, chemistry and sound calculations.
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How to use it
- Enter number x, base and custom base.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
log_b(x) = ln(x) / ln(b) by the change of base rule, with x > 0, b > 0 and b ≠ 1.
Example
Inputs: Number x = 81, Base = Other base, Custom base = 3. Result: Logarithm: 4; Natural log ln(x): 4.3944491547; Common log log10(x): 1.9084850189.
Limits and caveats
- Logs of zero or negative numbers are undefined in the reals and are not calculated.
- Results are rounded to 10 decimal places.
Questions about this tool
What is the difference between log and ln?
log usually means base 10, while ln is the natural log to base e, about 2.71828.
How do I get a log to a base my calculator lacks?
Use change of base: divide ln(x) by ln(b). Or choose "Other base" here and enter it directly.
Why is there no log of zero?
No power of a positive base equals zero; the value heads toward negative infinity without reaching it.