import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

def g(x, c):
    return (x**(1/2**20) - 1) * c

x = np.logspace(0.01, 90)

pars, cov = curve_fit(g, x, np.log10(x), p0=(2.27e5), maxfev=int(1e4))

plt.plot(x, np.log10(x))
plt.plot(x, g(x, *pars))
plt.semilogx();

print(f'(x^(1/2^20) - 1) * {pars[0]:.2f}')
print(g(364, pars[0]), np.log10(364), g(364, 455356) - np.log10(364))