Log Calculator · Practical guide
Log Base 2 Calculator
Find the binary logarithm of any positive number — set the base to 2 and get the result, inverse, and formula.
At a glance
The Quick Answer
Log base 2 of a number x answers the question: "2 raised to what power equals x?" For example, log2(1024) = 10, because 2^10 = 1,024. To compute any binary logarithm above, enter your number and set the base to 2. The calculator applies the change of base formula log2(x) = ln(x) / ln(2) automatically.
Interactive tool
Log Calculator
Enter your own values, then compare the result with the examples below.
Results
A Worked Example: log2(10)
Most calculators lack a log2 button, so use the change of base formula: log2(10) = ln(10) / ln(2) = 2.302585 / 0.693147 = 3.321928. Check it with the inverse: 2^3.321928 = 10 — exactly what the inverse row of this calculator shows.
Common Log Base 2 Values
| x | log2(x) | Because |
|---|---|---|
| 2 | 1 | 2^1 = 2 |
| 8 | 3 | 2^3 = 8 |
| 16 | 4 | 2^4 = 16 |
| 256 | 8 | 2^8 = 256 |
| 1,024 | 10 | 2^10 = 1,024 |
| 65,536 | 16 | 2^16 = 65,536 |
Why Binary Logarithms Matter
Log base 2 appears everywhere in computing. The number of bits needed to represent N values is log2(N) rounded up: 256 values need log2(256) = 8 bits. It also counts repeated halving — you can split 1,000 in half about log2(1000) = 9.97, so 10 times, before reaching 1 or less. That is why binary search on a million sorted items takes at most 20 steps (log2(1,000,000) = 19.93).
Frequently Asked Questions
What is log base 2 of 1024?
log2(1024) = 10, because 2 raised to the 10th power equals 1,024.
How do I calculate log base 2 without a log2 button?
Use the change of base formula: log2(x) = ln(x) / ln(2) or log2(x) = log10(x) / log10(2). This calculator does it for you when you set the base to 2.
Can log base 2 of a number be negative?
Yes, when x is between 0 and 1. For example, log2(0.5) = -1 because 2^-1 = 0.5. The number x itself must always be positive.
What is log2 of 1?
log2(1) = 0, because any base raised to the power 0 equals 1.