It has nothing to do with being a log chart or not. If you "break the axis", you give the impression of greater change than is actually contained in the graph. As the graph now stands, it appears that there is this wild swing with a huge upward movement. If you started the axis at zero, it would almost look like a horizontal line precisely because of the huge blank space at the bottom. People with foregone conclusions draw graphs like this to try and make a point where none exists.
Al Gore did the same thing with his temperature data. It has the same huge upward swing over time, making it look like an inverted hockey stick with this ominous uptick in temperature over the past several decades. The problem is that the vertical axis was "broken" and the units were in very small units (hundredths of a degree, I think). As a result, a half a degree change in temperature was made to look like huge upswing. When you set the axis to 0 (or 32 degrees, since many temperature charts start at freezing), the temperature line was virtually horizontal making the data look normal. Since that wasn't the message Al was trying to get across, he broke the axis to make the swing look more dramatic. I'm always suspect when I see such graphs.
Oh brother. If the graph having a blank inch or two at the bottom throws you, maybe this is a little to complex for you.