plot_log_small_ticks.py

import numpy as np
from matplotlib import pyplot as plt
import matplotlib as mpl

f, ax = plt.subplots()

x = np.geomspace(.01, 100)
y = x
ax.plot(x, y)
ax.set_xscale('log')


def func(a, b):
    b = int(np.log10(a))

    aa = f'{a:e}'

    s = str(aa)[0]

    ss = None

    if int(s) < 8:
        ss = f'$^{s}$'
    return ss


# ax.xaxis.set_major_locator(mpl.ticker.LogLocator(base=10.0, numticks=25,subs=(.2,.3,.4,.5,.6,.7,1)))

lg = mpl.ticker.FuncFormatter(func)

# lg = mpl.ticker.LogFormatterExponent()
ax.xaxis.set_minor_formatter(lg)

ax.grid(which='both')