NumPy: Logarithm with base n

Question

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?

Nudicaul

Answer 1

If you have numpy 1.23 or later, you can use np.emath.logn:

import numpy as np
array = np.array([74088, 3111696])  # = [42^3, 42^4]
base = 42
exponent = np.emath.logn(base, array)  # = [3, 4]

---

If your version of numpy is older:

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]

Which uses the logarithm base change rule:

Nudicaul

I cant understand why base isn't a parameter in numpy's log... I'm always coming back here... – Popper

"When will I ever use this?" -Student – Sissie

@Popper Same, plus I'm confused why there's a totally different positional parameter, out, so when naively switching math.log(number, base) to np.log(array, base), you get confusing errors like TypeError: 'float' object does not support item assignment or TypeError: return arrays must be of ArrayType. Apparently all ufuncs have the out parameter, but if it were keyword-only, it'd be so much simpler. – Amazonas

Answer 2

Numpy's base n logarithm function is np.emath.logn.

import numpy as np
arr = np.array([74088, 3111696])      # = [42^3, 42^4]
base = 42
np.emath.logn(base, arr)              # array([3., 4.])

np.emath.logn(14, 14**3)              # 3.0

Note that unlike math.log, the base is the first argument. Also, unlike math.log, it can handle negative numbers (returns a complex number).

Infantilism