I understand the general idea of loglog plots and their purpose but I have a few technical difficulties.
I know that:
- The axis of a log plot are still x and y but are scaling differently. So a point $p_1=(1,2)$ in linear plot still is located at $(1,2)$ but on a new scale.
- The new scale will change the shape of our graph because of change of scale.
Difficulties
Power Functions are linear functions in log-log plots ... When working with power functions like $f(x) = x^2$ so we can take $log$ on both sides and we end up with $log(y) = 2 log(x)$ I know this is linear function in the $log(y)$ vs $log(x)$ plane but why it is so in the y vs x plane with log-log scaling?
Fiddling with MATLAB it happens that if we have a set of points $p_k = (x_k,y_k)$ for $k=1,2,..K$ then plotting loglog(x,y) where $x,y\in\mathbb{R}^k$ hold the coordinates and plotting plot(log(x),log(y)) both give the same shape of the function (clearly different values but same general shape) ... Why is that ?