Log Base 2 Calculator
Enter x — get log₂(x) with full change-of-base working, a 2log₂(x) = x proof check, and related values.
log₂() =
Show your work (change of base)
Verification: 2log₂(x) = x
Related values
Worked examples
8 = 2³ — three doublings of 1.
1024 = 2¹⁰ — why 1024 bytes is a kibibyte (KiB).
0.5 = 2⁻¹ — one halving below 1.
Not a power of two. Change of base: log2(10) = ln(10) / ln(2) = 2.30258509299 / 0.69314718056 = 3.32192809489
Frequently asked questions
What is log base 2 of 8?
log2(8) = 3, because 2 raised to the power of 3 equals 8 (2 x 2 x 2 = 8).
What is log2(1024)?
log2(1024) = 10, because 2^10 = 1024. This is why 1024 bytes is called a kibibyte (KiB).
What is log2(0.5)?
log2(0.5) = -1, because 2^(-1) = 1/2 = 0.5.
What is log base 2 of 10?
log2(10) = 3.3219280949 (full value 3.32192809489). Change of base: log2(10) = ln(10) / ln(2) = 2.30258509299 / 0.69314718056 = 3.32192809489.
What is the change-of-base formula for log2?
log2(x) = ln(x) / ln(2) = log10(x) / log10(2). This calculator shows every step of the natural-log version, and you can verify the answer with the 2^log2(x) = x check.
What is log2(1)?
log2(1) = 0, because 2^0 = 1. The log of 1 is 0 in every base.
What is log2(0) or log2 of a negative number?
Both are undefined. Log base 2 is only defined for x > 0. This calculator rejects 0, negative numbers, and non-numeric input with a clear error.
What is binary logarithm used for?
Binary logarithms measure how many doublings or halvings it takes to reach a number: bits of information (entropy), binary search steps (log2(n)), music octaves, binary tree height, and big-O complexity like O(log n).
How do you check a log2 answer?
Raise 2 to the answer: 2^log2(x) must equal x. This calculator performs that round-trip check automatically on every result.
What is log2(2)?
log2(2) = 1, because 2^1 = 2.
How is this different from a natural log or log10 calculator?
Only the base differs. log2(x) = ln(x)/ln(2), and the related-values panel shows the equivalent ln(x) and log10(x) next to the log2 result for comparison.
Where do I solve an equation like 2^x = 32 or log2(x) = 5?
That is a different job: solving for an unknown. This tool evaluates log2(x) for a known x. To solve exponential or logarithmic equations step by step, use our exponential-logarithmic-equations-calculator.
Free tool by NRTechStudio