Specifying bins=8 in the hist call means that the range between the minimum and maximum value is divided equally into 8 bins. What is equal on a linear scale is distorted on a log scale.
What you could do is specify the bins of the histogram such that they are unequal in width in a way that would make them look equal on a logarithmic scale.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
x = [2, 1, 76, 140, 286, 267, 60, 271, 5, 13, 9, 76, 77, 6, 2, 27, 22, 1, 12, 7,
19, 81, 11, 173, 13, 7, 16, 19, 23, 197, 167, 1]
x = pd.Series(x)
# histogram on linear scale
plt.subplot(211)
hist, bins, _ = plt.hist(x, bins=8)
# histogram on log scale.
# Use non-equal bin sizes, such that they look equal on log scale.
logbins = np.logspace(np.log10(bins[0]),np.log10(bins[-1]),len(bins))
plt.subplot(212)
plt.hist(x, bins=logbins)
plt.xscale('log')
plt.show()
