In this article, we’ll explain how to use the logarithmic scale in Matplotlib.

The logarithmic scale is useful for plotting data that includes very small numbers and very large numbers because the scale plots the data so you can see all the numbers easily, without the small numbers squeezed too closely.

(This article is part of our Data Visualization Guide. Use the right-hand menu to navigate.)

Logarithms

First, let’s review a little high school math. A logarithm is a way to make a large number appear small by looking at it as a power of 10. There are other logarithm bases besides 10, like the natural logarithm used in mathematics, which is given by the constant e=2.718…. But, for our purposes, we will use base 10 logarithms.

In short:

log₁₀x = y means 10 raised to power y equals x, i.e., 10 ** y = x. So log₁₀100=2 because 10**2 = 100.

The logarithmic scale in Matplotlib

A two-dimensional chart in Matplotlib has a yscale and xscale. The scale means the graduations or tick marks along an axis. They can be any of:

• matplotlib.scale.LinearScale—These are just numbers, like 1, 2, 3.
• matplotlib.scale.LogScale—These are powers of 10. You could use any base, like 2 or the natural logarithm value, which is given by the number e. Using different bases would narrow or widen the spacing of the plotted elements, making visibility easier.
• matplotlib.scale.SymmetricalLogScale and matplotlib.scale.LogitScale—These are used for numbers less than 1, in particular very small numbers whose logarithms are very large negative numbers.