The math.log2() function in Python is used to compute the base-2 logarithm of a given number. It is part of the math module, which provides access to various mathematical functions.

Syntax

import math
result = math.log2(x)

• x: A positive numeric expression (integer or float) for which you want to calculate the base-2 logarithm.

Return Value

• Returns the logarithm of x to base 2 as a float.
• If x is less than or equal to zero, a ValueError will be raised.

Examples

1. Calculating the base-2 logarithm of a positive integer:

   import math
   
   result = math.log2(8)
   print(result)  # Output: 3.0 (because 2^3 = 8)
   

2. Calculating the base-2 logarithm of a decimal:

   result = math.log2(0.5)
   print(result)  # Output: -1.0 (because 2^-1 = 0.5)
   

3. Calculating the logarithm of a larger number:

   result = math.log2(32)
   print(result)  # Output: 5.0 (because 2^5 = 32)
   

4. Handling values less than or equal to zero: If you try to calculate the logarithm of a non-positive number, a ValueError will be raised.

   try:
       result = math.log2(-4)
   except ValueError as e:
       print(e)  # Output: math domain error
   

5. Using math.log2() in expressions: You can use math.log2() in combination with other mathematical operations:

   value = 64
   result = math.log2(value) + 1
   print(result)  # Output: 7.0
   

Summary

• The math.log2() function computes the logarithm of a positive number to base 2.
• It returns a float representing the logarithmic value.
• This function is commonly used in computer science and information theory, particularly in contexts like calculating binary tree depths, analyzing algorithm complexity, and data encoding.