Log Base 2 Calculator
Result:
Calculation Details:
What is Log Base 2 (log₂)?
The binary logarithm (log₂) answers:
“How many times must we multiply 2 to get a given number?”
Mathematically:
If log₂(x) = y, then 2ʸ = x.
Key Properties:
✔ log₂(1) = 0 (since 2⁰ = 1)
✔ log₂(2) = 1 (since 2¹ = 2)
✔ Used in computer science (binary trees, Big-O notation)
✔ Helps measure algorithm efficiency (e.g., binary search = O(log₂ n))
User Guide for Log Base 2 Calculator:
How to Use the Calculator
- Enter a Positive Number (e.g.,
8,256,0.5) - Click “Calculate Log₂(x)”
- View Results:
- Exact log₂(x) value (6 decimal places)
- Step-by-step explanation
Example Calculations
| Input (x) | log₂(x) ≈ | Explanation |
|---|---|---|
| 1 | 0 | 2⁰ = 1 |
| 8 | 3 | 2³ = 8 |
| 1024 | 10 | 2¹⁰ = 1024 |
| 0.5 | -1 | 2⁻¹ = 0.5 |
Common Applications
🔹 Computer Science: Binary trees, algorithm analysis
🔹 Data Compression: Measuring entropy in bits
🔹 Audio Engineering: Decibel (dB) calculations
Try It Now!
Use the calculator above to explore log₂(x) for any positive number.
Perfect for programmers, engineers, and math students! 🖥️🎯