Plotting Log-normal scale in matplotlib

Question

I've got these two lists which are x,y points to be plotted:

microns = [38,  45,  53,  63,  75,  90, 106, 125, 150, 180]
cumulative_dist = [25.037, 32.577, 38.34, 43.427, 51.57,56.99, 62.41,69.537,74.85, 81.927]

The thing is I need to plot them following the scale showed in the image below (more info here), which is a log-normal plot.

How can I get this scale using matplotlib?

I guess I'll need to use matplotlib.scale.FuncScale, but I'm not quite sure how to get there.

Answer 1

After David's insightful comment I've read this page and managed to plot the Figure the way I wanted.

from matplotlib.ticker import ScalarFormatter, AutoLocator
from matplotlib import pyplot
import pandas as pd
import probscale
fig, ax = pyplot.subplots(figsize=(9, 6))
microns = [38,  45,  53,  63,  75,  90, 106, 125, 150, 180]
cumulative_dist = [25.037, 32.577, 38.34, 43.427, 51.57,56.99, 62.41,69.537,74.85, 81.927]
probscale.probplot(pd.Series(microns, index=cumulative_dist), ax=ax, plottype='prob', probax='y', datascale='log',
                   problabel='Cumulative Distribution (%)',datalabel='Particle Size (μm)',
                   scatter_kws=dict(marker='.', linestyle='none', markersize=15))
ax.set_xlim(left=28, right=210)
ax.set_ylim(bottom=1, top=99)
ax.set_title('Log Normal Plot')
ax.grid(True, axis='both', which='major')
formatter = ScalarFormatter()
formatter.set_scientific(False)
ax.xaxis.set_major_formatter(formatter)
ax.xaxis.set_minor_formatter(formatter)
ax.xaxis.set_major_locator(AutoLocator())
ax.set_xticks([])  # for major ticks
ax.set_xticks([], minor=True)  # for minor ticks
ax.set_xticks(microns)
fig.show()