What is log₂ used for?
Bits, binary trees, algorithm complexity, and MIDI/octave math among other uses.
Log Base 2 Calculator
Compute log₂(x)—common in computer science, information theory, and binary scales.
Enter a positive number
Provide x > 0 to evaluate log₂(x).
About this calculator
How to use Log Base 2 Calculator, plus the formulas and logic behind the results.
Tool description
log₂(x) answers “2 to what power equals x?” It equals ln(x)/ln(2).
How to use
- Enter a positive value for x.
- Select Calculate.
- Read log₂(x) and optional powers-of-two context.
- Adjust x for another evaluation.
Formulas & reference
log₂(x) = ln(x) / ln(2)2^{log₂(x)} = x for x > 0
Powers of two
- log₂(1) = 0
- log₂(2) = 1
- log₂(8) = 3
- log₂(1024) = 10
Calculation logic
Rejects non-positive x, then computes log(x)/log(2) and formats the result.
Only positive real arguments are supported.
Log Base 2 Calculator FAQ
Common questions about this calculator and how to use the results.
Can x be a fraction?
Yes, as long as it is positive (e.g. log₂(0.5) = −1).
Is log₂(0) defined?
No. Logarithms are undefined at zero.
How do calculators compute it?
Usually via change of base: ln(x)/ln(2).
What if x is not a power of two?
You still get a real (often non-integer) result.
Is lg the same as log₂?
In some CS texts lg means log₂; elsewhere lg may mean log₁₀.