What does a gradient of 0.5 show on a log log graph?

Answer 1

If y=xn, then log y =nlogx and n indicates the power in the power function. If one has a set of data [x,y] and if a plot of logy vs logx yields a straight line or one reasonably so, then the slope (gradient) of the line reveals the power relation between x and y

Answer 2

A gradient of 0.5 on a log-log graph indicates a power-law relationship between the variables being measured. This means that the relationship between the variables is proportional to the square root of one variable raised to the power of 0.5.