Calculate logarithms to any base — including log base 2, natural log and log base 10 — plus antilogs and change-of-base conversions.
Quick check: log₂ 8 = 3 because 2³ = 8. Try the presets — log 2, log base 2 and log base 10 are all covered.
Antilog: if log₂ y = 10, then y = 2¹⁰ = 1024.
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How to use this tool
Logarithm finds the exponent; antilog raises the base to an exponent.
Pick base 2, 10, e (natural log) or a custom base, then type the value.
Alongside your answer you also get ln, log₁₀ and log₂ for the same value.
The check row raises the base to the answer — it should return your original value.
Formula & worked example
log₂ 8 = 3 because 2³ = 8. Likewise log₁₀ 1000 = 3 because 10³ = 1000, and the antilog 2¹⁰ = 1024.
Limitations — read this before you rely on it
Logarithms are only defined for positive values and for bases greater than 0 and not equal to 1. Results are rounded to 6 decimal places for display; the underlying values are exact.
Frequently asked questions
log₂(x) answers: '2 to what power gives x?' So log₂ 8 = 3, because 2³ = 8. It is widely used in computing and information theory.
ln is log base e (≈ 2.718), used in maths and science; 'log' on most calculators means log base 10. This calculator shows both, plus log₂.
The reverse of a logarithm: the antilog of y in base b is b^y. For example, the antilog of 10 in base 2 is 1024.
No real power of a positive base gives 0 or a negative result, so the logarithm is undefined there in real numbers.
Any logarithm can be rewritten with another base: log_b(x) = ln(x) ÷ ln(b). That is how this calculator handles custom bases.