I have data of a function that goes like $f(x)\propto x ^\alpha $ for a certain range of $x$ and like $f(x)\propto x^\beta$ for another one. It is common in the literature to make a log log plot and then fit two straight lines in the corresponding regimes to show the different exponents. I was wondering how one can achieve this in Mathematica. Basically, the questions are

1) How to make a linear fit on loglog data?

2) How to make and show multiple linear fits on different ranges of the data?