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. It's widely used in computer science, information theory, and mathematics.

2. How Does the Calculator Work?

The calculator uses the logarithmic identity:

Where:

• \( x \) — Input value (must be positive)
• \( \ln \) — Natural logarithm (base e)

Explanation: The formula converts the log base 2 calculation into a ratio of natural logarithms, which can be easily computed.

3. Applications of Log Base 2

Details: Log base 2 is essential in computer science (binary trees, algorithm complexity), information theory (bits), and signal processing (decibels).

4. Using the Calculator

Tips: Enter any positive number to calculate its log base 2. The result is unitless. Input must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is log base 2 important in computing?
A: Computers use binary (base 2) systems, so log₂ directly relates to bits, binary trees, and algorithm efficiency.

Q2: What's the difference between log₂ and ln?
A: log₂ uses base 2 while ln (natural log) uses base e (≈2.718). They're related by the constant factor ln(2).

Q3: What does log₂(1) equal?
A: log₂(1) = 0, since 2⁰ = 1. This is true for any log base of 1.

Q4: Can log base 2 be negative?
A: Yes, when 0 < x < 1. For example, log₂(0.5) = -1 since 2⁻¹ = 0.5.

Q5: How is log base 2 used in information theory?
A: It measures information in bits. The number of bits needed to represent N distinct messages is ⌈log₂N⌉.