Log-Log plots

1. Introduction

The aim of this article is to provide an understanding of the log-log plots.

2. Log-log plots

Many quantities in engineering can be described by equations of the form,

It is, though, not easy to distinguish between graphs of different power laws.

Consider the data below;

Figure: Linear, quadratic and quartic plots

It is not easy to see that the red points lie on a quadratic ( y = Ax^2) and the blue data lie on a quartic (y =  Ax^4). It is however clear that the black points lie on a straight line!

Log-Log plots enable to recast the power curves as straight lines and so extract both constants  n and A.in the above equation.

3. Example of log-log plots

Consider the equation,

This is a power curve, but if we take the logarithm of each side we obtain:

If Y = log(y) and X = log(x) then Y = nX. This shows the linear relationship. Plotting Y against X, i.e., log(y) against log(x), leads to a straight line as below;

Figure : Log-Log plot

Here n is the slope of the line. Thus: from a log-log plot, we can directly read off the power n.