DOC: Improve log scale example

- Remove https://matplotlib.org/stable/gallery/scales/semilogx_demo.html
  It is redundant to the other log scale example.
- Explain that semilogx/semilogy/loglog are shortcuts.
- Tune data/visualization

Author: timhoffm

galleries/examples/scales/log_demo.py

@@ -1,34 +1,41 @@
 """
-========
-Log Demo
-========
+=========
+Log scale
+=========
 
 Examples of plots with logarithmic axes.
+
+You can set the x/y axes to be logarithmic by passing "log" to `~.Axes.set_xscale` /
+`~.Axes.set_yscale`.
+
+Since plotting data on semi-logarithmic or double-logarithmic scales is very common,
+the functions `~.Axes.semilogx`, `~.Axes.semilogy`, and `~.Axes.loglog` are shortcuts
+for setting the scale and plotting data; e.g. ``ax.semilogx(x, y)`` is equivalent to
+``ax.set_xscale('log'); ax.plot(x, y)``.
 """
 
 import matplotlib.pyplot as plt
 import numpy as np
 
-# Data for plotting
-t = np.arange(0.01, 20.0, 0.01)
+fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, layout='constrained')
 
-# Create figure
-fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2)
-
-# log y axis
-ax1.semilogy(t, np.exp(-t / 5.0))
-ax1.set(title='semilogy')
+# log x axis
+t = np.arange(0.01, 10.0, 0.01)
+ax1.semilogx(t, np.sin(2 * np.pi * t))
+ax1.set(title='semilogx')
 ax1.grid()
 
-# log x axis
-ax2.semilogx(t, np.sin(2 * np.pi * t))
-ax2.set(title='semilogx')
+# log y axis
+x = np.arange(10)
+ax2.semilogy(x, 2**x, 'x:', base=2)
+ax2.set(title='semilogy with base 2')
 ax2.grid()
 
+
 # log x and y axis
-ax3.loglog(t, 20 * np.exp(-t / 10.0))
-ax3.set_xscale('log', base=2)
-ax3.set(title='loglog base 2 on x')
+x = np.array([1, 10, 100, 1000, 10000])
+ax3.loglog(x, 5 * x, 'o--')
+ax3.set(title='loglog')
 ax3.grid()
 
 # With errorbars: clip non-positive values
@@ -38,10 +45,9 @@
 
 ax4.set_xscale("log", nonpositive='clip')
 ax4.set_yscale("log", nonpositive='clip')
-ax4.set(title='Errorbars go negative')
+ax4.set(title='loglog with errorbars going negative')
 ax4.errorbar(x, y, xerr=0.1 * x, yerr=5.0 + 0.75 * y)
 # ylim must be set after errorbar to allow errorbar to autoscale limits
 ax4.set_ylim(bottom=0.1)
 
-fig.tight_layout()
 plt.show()