Log Calculator
Calculate logarithms in any base with this free online log calculator: log base 10, natural log (ln), log base 2, antilog and change of base.
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Part of the toolkit
How to use Log Calculator
- 1Choose Logarithm, or Antilog to raise the base to a power
- 2Enter the base (any positive number except 1, or e) and the number
- 3Read the result plus ln, log₁₀ and log₂ of the number, and copy it
Frequently asked questions
What is a logarithm?▾
log_b(x) is the power you raise b to in order to get x. log₁₀(1000) = 3 because 10³ = 1000, and log₂(8) = 3 because 2³ = 8.
How do I calculate a log with any base?▾
Use the change-of-base formula: log_b(x) = ln(x) ÷ ln(b). For example log₅(125) = ln 125 ÷ ln 5 = 3.
What is ln?▾
The natural logarithm — log base e, where e ≈ 2.71828. ln(e) = 1 and ln(1) = 0.
What is an antilog?▾
The inverse of a logarithm: antilog_b(y) = b^y. The antilog base 10 of 2 is 100.
Why can't I take the log of 0 or a negative number?▾
No real power of a positive base gives 0 or a negative number, so logarithms are only defined for x > 0.
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