The math.log() function in Python is used to calculate the logarithm of a number. You can compute logarithms with different bases using this function, with the default base being $e$ (Euler's number, approximately 2.71828).

Syntax

import math
result = math.log(x[, base])

• x: The number for which you want to calculate the logarithm. It must be a positive number.
• base (optional): The base of the logarithm. If not provided, the natural logarithm (base $e$) is calculated.

Return Value

• Returns the logarithm of x to the specified base. If no base is specified, it returns the natural logarithm of x.

Examples

1. Calculating the natural logarithm (base $e$):

   import math
   
   result = math.log(10)
   print(result)  # Output: 2.302585092994046 (approximately)
   

2. Calculating the logarithm with a specified base: For example, calculating the logarithm of 1000 with base 10:

   result = math.log(1000, 10)
   print(result)  # Output: 3.0 (because 10^3 = 1000)
   

3. Using base 2 for binary logarithm:

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

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.log(-5)
   except ValueError as e:
       print(e)  # Output: math domain error
   

5. Using logarithms in expressions: You can use the math.log() function in more complex mathematical expressions:

   value = 20
   result = math.log(value) + 5
   print(result)  # Output: 7.302585092994046 (approximately)
   

Summary

• The math.log() function computes the logarithm of a positive number.
• You can specify a custom base; if not provided, it calculates the natural logarithm (base $e$).
• The return type is always a float.
• This function is essential in various mathematical and scientific computations, including growth models, finance, and information theory.