Logarithm calculator
Work out logarithms in any base and see how the change of base formula gets the answer. Students in algebra, chemistry and computer science use it to check pH, decibel and binary math.
- Runs in your browser
- Free, no account needed
- Copy or download the result
Result
Example
Calculation: Logarithm: log base b of x Number x: 1000 Base: 10 (common log) Custom base: 3
log base 10 of 1000 = 3 Check: 10^3 = 1000 Change of base: ln(1000) / ln(10) = 6.90775527898 / 2.30258509299 = 3 Common log, log10: 3 Natural log, ln: 6.90775527898 Binary log, log2: 9.96578428466 Results are rounded to 12 significant digits.
How to use the logarithm calculator
- Choose a Calculation: Logarithm or Antilog.
- Type the Number x and pick a Base, or choose Custom base and fill in the Custom base field.
- Press Run to see the result, a check and the change of base steps.
- Press Copy result or Download to keep the answer.
How it works
log base b of x is the power you raise b to in order to get x. The change of base formula is log base b of x = ln(x) / ln(b).
x must be greater than zero, and a custom base must be positive and not 1.
Antilog mode computes b raised to x. Very large antilogs are shown in scientific notation.
Results use floating point and are rounded to 12 significant digits, which hides tiny rounding errors such as 2.9999999999999996.
Everything runs in your browser. Your input is not uploaded or stored.
Questions and answers
What is the difference between log and ln?
log usually means base 10, and ln means the natural log with base e, about 2.71828.
How do I calculate a log with a different base?
Use the change of base formula: log base b of x = ln(x) / ln(b). For example, log base 3 of 81 = ln(81) / ln(3) = 4.
What is an antilog?
An antilog undoes a logarithm. The antilog of 3 in base 10 is 10^3 = 1000.
Why can't I take the log of zero or a negative number?
No real power of a positive base gives zero or a negative number, so those logarithms are undefined in real numbers.