1. What is Logarithm Base 2?

The logarithm base 2 (log₂) of a number is the exponent to which the base 2 must be raised to obtain that number. Mathematically, if log₂(x) = y, then 2ʸ = x.

2. How Does the Calculator Work?

The calculator uses the logarithmic equation:

Where:

• \( x \) — The input number (must be positive)
• \( y \) — The result (exponent to which 2 must be raised to get x)

Explanation: The calculator computes the logarithm using PHP's built-in log function with base 2.

3. Importance of Log Base 2 Calculation

Details: Log base 2 is particularly important in computer science (binary systems, information theory), music theory, and many areas of mathematics and engineering.

4. Using the Calculator

Tips: Enter any positive number (x) to calculate its log base 2. The result (y) will show the exponent needed for 2ʸ = x.

5. Frequently Asked Questions (FAQ)

Q1: What is log₂(1)?
A: log₂(1) = 0, because 2⁰ = 1.

Q2: What is log₂(2)?
A: log₂(2) = 1, because 2¹ = 2.

Q3: Can I calculate log₂(0)?
A: No, log₂(0) is undefined as there's no exponent that makes 2ʸ = 0.

Q4: What about negative numbers?
A: Logarithms of negative numbers are not real numbers (they're complex numbers).

Q5: How is this different from natural log (ln)?
A: log₂ uses base 2 while natural log (ln) uses base e (≈2.71828). They're related by the formula: log₂(x) = ln(x)/ln(2).