Caption: An example of a log-log plot.
Logarithmic plots are useful for showing a function over many orders of magnitude by allowing you to see the functional behavior on many scales simultaneously---at the cost of making the function a bit distorted by linear-scale standards.
On linear-scale plots, much of the behavior of function that varies tremendously with scale (like the function in the figure) is off the plot or is squashed down to the x-axis and/or y-axis.
Many linear-scale plots may be needed to show the whole functional behavior in roughly equal detail.
For example for function in the figure, if you displayed the whole function on a linear-scale plot, all the lower left behavior would be squashed into the x-axis and y-axis, and would be invisible or nearly invisible.
The log-log plot allows us to see that behavior easily.
Credit/Permission: © David Jeffery,
2004 / Own work.
Image link: itself.
File: Mathematics file:
log_plot.html.