If there is a exponential relationship $y = e^x$ and we take the logarithm of this we can see a linear relationship $\ln (y) = x$. So we could plot the logarithm of the y-axis values against the x values. Why does matlab do loglog plots, where the x-axis is also presented in logarithms? I see many plots where this is done.
Wouldn't using semilogy suffice? Or does using loglog or semilogy actually make no difference for a particular reason?
Best Answer
Besides looking for exponential relationships, one might also want to track power law relationships. As Didier and I pointed out, log-log plots are ideal for the task because they reduce any power law relationship to a linear relationship. The exponent then becomes the slope of the graphic, as seen from
$$y=c x^a \Leftrightarrow \log y = a \log x + \log c$$
Also see this question.