Can you please provide a picture? Might be easier to evaluate what you're after that way.

Default:

With minor ticks:

cb.ax.minorticks_on() works in a different way:

Thanks, @Kojoley. cb.ax.minorticks_on() gives evenly spaced minor tick marks in log space, which is not what I want. In my opinion, the default should be evenly spaced minor tick marks in linear space, which translate to unevenly spaced minor tick marks in log space.

The trouble is, I have tried using cb.ax.minorticks_on() and a LogLocator to place the minor tick marks where I want them, but I cannot get them to work together. (The problem might be that the color bar expects tick marks to be normalized from 0 to 1.) The only method that works for me is

p = plt.pcolormesh(X, Y, Z, norm=LogNorm(), vmin=1e-2, vmax=1e2)
cb = plt.colorbar(p, ax=ax, orientation='horizontal', aspect=10)
minorticks = p.norm(np.hstack([np.arange(2, 10, 1)/10.0, np.arange(2, 10, 1)/1.0]))
cb.ax.xaxis.set_ticks(minorticks, minor=True)

Thus, this seems to be a little more than a simple change to the default settings.

attn @efiring

On current v2.x, this:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm

x = np.linspace(1,10,10)
y = np.linspace(1,10,10)
X, Y = np.meshgrid(x,y)
Z = np.abs(np.cos(X**2 - Y**2) * X**2 * Y)
f, ax = plt.subplots()
p = plt.pcolormesh(X, Y, Z, norm=LogNorm(), vmin=1e-2, vmax=1e2)
cb = plt.colorbar(p, ax=ax, orientation='horizontal', aspect=10)
plt.show()

looks like this by default:

so I guess this has been fixed?

Closed by #7438.

I am glad to see that minor ticks are placed properly now, but tick length on minor tick should be shorter than major ticks, IMHO. That's how it used to be (see Kojoley's Sep 20th post). Perhaps the minor tick length is just a rcParams setting...

No, it will take more work to fix that. It won't happen for 2.0. It requires substantial change to the colorbar tick-handling, which differs from normal axis tick handling because there is an additional transformation between the colorbar tick values and the axis coordinates. The colorbar does not support major and minor ticks; it has only major ticks. It has a single ticks kwarg and a single format kwarg, together with the machinery to use their values, or suitable defaults based on the norm. Directly setting the minor ticks as in the example at the top of this issue will not work correctly in general because the data limits don't necessarily correspond to the (0, 1) colorbar axis coordinates.
This is related to the confusing intersection among scales, transforms, norms, tickers, and the necessarily unique characteristics of a colorbar. I would prefer to see it handled in the course of a larger code cleanup and refactoring rather than by merely adding a bunch of code to the already-complex colorbar. (Actually, my mind is wavering; hacking minor ticks into the colorbar is conceptually straightforward, and probably the API changes--adding 2 kwargs--would be the same as we would end up with after a major re-write.)
I will open a separate issue for this.

Ok. Thank you for the detailed reply. I probably would have spent 30 minutes figuring that out on my own.