You can use the Axes.set_yscale method. That allows you to change the scale after the Axes object is created. That would also allow you to build a control to let the user pick the scale if you needed to.

The relevant line to add is:

ax.set_yscale('log')

You can use 'linear' to switch back to a linear scale. Here's what your code would look like:

import pylab
import matplotlib.pyplot as plt
a = [pow(10, i) for i in range(10)]
fig = plt.figure()
ax = fig.add_subplot(2, 1, 1)

line, = ax.plot(a, color='blue', lw=2)

ax.set_yscale('log')

pylab.show()

First of all, it's not very tidy to mix pylab and pyplot code. What's more, pyplot style is preferred over using pylab.

Here is a slightly cleaned up code, using only pyplot functions:

from matplotlib import pyplot

a = [ pow(10,i) for i in range(10) ]

pyplot.subplot(2,1,1)
pyplot.plot(a, color='blue', lw=2)
pyplot.yscale('log')
pyplot.show()

The relevant function is pyplot.yscale(). If you use the object-oriented version, replace it by the method Axes.set_yscale(). Remember that you can also change the scale of X axis, using pyplot.xscale() (or Axes.set_xscale()).

Check my question What is the difference between ‘log’ and ‘symlog’? to see a few examples of the graph scales that matplotlib offers.

You simply need to use semilogy instead of plot:

from pylab import *
import matplotlib.pyplot  as pyplot
a = [ pow(10,i) for i in range(10) ]
fig = pyplot.figure()
ax = fig.add_subplot(2,1,1)

line, = ax.semilogy(a, color='blue', lw=2)
show()

if you want to change the base of logarithm, just add:

plt.yscale('log',base=2) 

Before Matplotlib 3.3, you would have to use basex/basey as the bases of log

I know this is slightly off-topic, since some comments mentioned the ax.set_yscale('log') to be "nicest" solution I thought a rebuttal could be due. I would not recommend using ax.set_yscale('log') for histograms and bar plots. In my version (0.99.1.1) i run into some rendering problems - not sure how general this issue is. However both bar and hist has optional arguments to set the y-scale to log, which work fine.

references:

So if you are simply using the unsophisticated API, like I often am (I use it in ipython a lot), then this is simply

yscale('log')
plot(...)

Hope this helps someone looking for a simple answer! :).