NumPy: Logarithm with base n

python math numpy logarithm

Banana · Aug 6, 2014 · Viewed 78.6k times · Source

From the numpy documentation on logarithms, I have found functions to take the logarithm with base e, 2, and 10:

import numpy as np
np.log(np.e**3) #3.0
np.log2(2**3)   #3.0
np.log10(10**3) #3.0

However, how do I take the logarithm with base n (e.g. 42) in numpy?

Answer

To get the logarithm with a custom base using math.log:

import math
number = 74088  # = 42**3
base = 42
exponent = math.log(number, base)  # = 3

To get the logarithm with a custom base using numpy.log:

import numpy as np
array = np.array([74088, 3111696])  # = [42**3, 42**4]
base = 42
exponent = np.log(array) / np.log(base)  # = [3, 4]

As you would expect, note that the default case of np.log(np.e) == 1.0.

As a reminder, the logarithm base change rule is:

$\log_b(x)=\log_c(x)/\log_c(b)$