Log Base 2 Calculator
Calculate binary logarithms (log₂) and inverse calculations with detailed explanations
Binary Logarithm Calculator
Must be a positive number (x > 0)
log₂(x) = result
Powers of 2 Reference
Common Log₂ Values
Binary Logarithm Tips
log₂(1) = 0 for any base
log₂(2) = 1 by definition
Binary logarithms are used in computer science
Powers of 2 give integer results
Useful for bit calculations and data storage
Understanding Binary Logarithms (Log Base 2)
What is a Binary Logarithm?
The binary logarithm, denoted as log₂(x), is the logarithm with base 2. It answers the question: "To what power must we raise 2 to get the value x?" For example, log₂(8) = 3 because 2³ = 8.
Why Base 2?
- •Fundamental in computer science and digital systems
- •Used in information theory for measuring data in bits
- •Essential for binary search algorithms
- •Important in data compression and encoding
Calculation Methods
Change of Base Formula
Properties
- •log₂(a × b) = log₂(a) + log₂(b)
- •log₂(a / b) = log₂(a) - log₂(b)
- •log₂(a^n) = n × log₂(a)
- •2^(log₂(x)) = x (for x > 0)
Applications in Computer Science
Algorithm Analysis
Binary search has O(log₂ n) time complexity, meaning it takes log₂(n) steps to find an element.
Data Storage
To store n different values, you need ⌈log₂(n)⌉ bits. For example, 256 values need 8 bits.
Information Theory
Information content is measured in bits using log₂, where each bit represents one binary decision.