Log Base 2 Calculator

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Reviewed by: David Chen, CFA
Senior Financial Analyst & Computing Specialist

Need to find the binary logarithm of a number? Our log base 2 calculator provides instant, accurate results for computer science, information theory, and mathematical applications.

log base 2 calculator

Binary Logarithm log₂(x):
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log base 2 calculator Formula:

log₂(x) = log₁₀(x) / log₁₀(2)

Source: Wolfram MathWorld – Logarithm | Wikipedia – Binary Logarithm

Variables:

  • x: The positive real number you want to find the logarithm for.
  • log₂(x): The power to which the number 2 must be raised to obtain the value x.

Related Calculators:

What is log base 2 calculator?

A log base 2 calculator, also known as a binary logarithm calculator, determines the exponent needed to raise the base 2 to produce a specific number. This mathematical function is fundamental in computer science, where data is processed in bits (binary digits).

In information theory, log base 2 is used to measure entropy and information content. For example, if you have 8 possible outcomes, it takes log₂(8) = 3 bits to represent each outcome.

How to Calculate log base 2 calculator (Example):

Follow these steps to calculate the binary logarithm manually using a standard calculator:

  1. Identify your input value (e.g., x = 64).
  2. Find the common logarithm (log₁₀) of x: log₁₀(64) ≈ 1.80618.
  3. Find the common logarithm of the base (2): log₁₀(2) ≈ 0.30103.
  4. Divide the first result by the second: 1.80618 / 0.30103 = 6.
  5. The result is log₂(64) = 6.

Frequently Asked Questions (FAQ):

Can I calculate log base 2 of a negative number?
No, the logarithm of a negative number or zero is undefined in the set of real numbers. The input must be greater than zero.

What is log₂ of 1?
The result is always 0, because any non-zero number raised to the power of 0 equals 1 (2⁰ = 1).

Is log base 2 the same as ‘lb’?
Yes, ‘lb’ is the standard ISO notation for the binary logarithm (log base 2).

Why is log base 2 used in computer science?
It helps calculate the number of steps in binary search algorithms, the height of balanced trees, and data compression limits.

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