-22.0780076747 = A + B*2^{-x}
-24.3957157406 = A + B*3^{-x}
-25.4414515613 = A + B*4^{-x}

#!/usr/bin/env python
import numpy as np
from scipy.optimize import root

def your_funcs(X):

    A, B, x = X

    f = [21.7424698112-A-B*(1/2**x),
         22.4531418345-A-B*(1/3**x),
         23.8033967265-A-B*(1/4**x)]

    return f

sol = root(your_funcs, [1.0, 1.0, 1.0])
print(sol.x)

[ 22.66633613 -50.69139062 105.89893632]