A logarithmic axis is useful for displaying data with a large range of values. Sometimes these values are already on a log scale – e.g. the Richter scale is a log scale, as is decibels. You can plot this on a normal linear numeric axis. But sometimes your values can’t be easily converted to a log scale. Maybe you’re plotting wealth distribution. Or, in my case, particle size distributions, where the sizes can range from metres down to microns. When dealing with something like this, you need a log axis.