Caption: A log-log plot
of the power-law function
y = f(x) = [x**(-10)]*[(10**(20)],which in logarithmic form is
log(y) = log[f(x)] = -10*log(x) + 20.
Features:
In many log-log plots, just the powers are shown. If just the powers were shown for this plot, the x-axis values would run 0, 1, 2, 3 and the y-axis values would run -20, -15, -10, -5, 0, 5, 10, 15, 20.
To explicate, the general power-law function
y = a*x**phas the logarithmic form
log(y) = p*log(x)+a,which is a straight line, where p is the slope and a y-intercept.
Since a log-log plot automatically converts function logarithmic form, it converts power-law functions into straight lines: QED.
Since power-law functions are very common in science and straight lines are easy to understand, the effect of log-log plots on power-law functions is very useful.