The example here What is the difference between 'log' and 'symlog'? nicely shows how a linear scale at the origin can be used with a log scale elsewhere. I
This solution makes an addition to cphlewis's answer so that there is a smooth transition, and the plot appears to have consistent tick markers. My change adds these three lines:
axLin.spines['bottom'].set_visible(False)
axLin.xaxis.set_ticks_position('top')
plt.setp(axLin.get_xticklabels(), visible=False)
In total, the code is
# linear and log axes for the same plot?
# starting with the histogram example from
# http://matplotlib.org/mpl_toolkits/axes_grid/users/overview.html
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
import numpy as np
# Numbers from -50 to 50, with 0.1 as step
xdomain = np.arange(-50,50, 0.1)
axMain = plt.subplot(111)
axMain.plot(xdomain, np.sin(xdomain))
axMain.set_yscale('log')
axMain.set_ylim((0.01, 0.5))
axMain.spines['top'].set_visible(False)
axMain.xaxis.set_ticks_position('bottom')
divider = make_axes_locatable(axMain)
axLin = divider.append_axes("top", size=2.0, pad=0, sharex=axMain)
axLin.plot(xdomain, np.sin(xdomain))
axLin.set_xscale('linear')
axLin.set_ylim((0.5, 1.5))
# Removes bottom axis line
axLin.spines['bottom'].set_visible(False)
axLin.xaxis.set_ticks_position('top')
plt.setp(axLin.get_xticklabels(), visible=False)
plt.title('Linear above, log below')
plt.show()