linéarisation of a quasi-linear function with logarithmic scale and logarithmic axis.

If the graph in the log-log-plot should be a straight line we know that the function must be y=a*x^b.
But its better to fit the logarithmic data to a linear function rather than fitting the original data to a power function. Fitting the original data would mean that the deviation from the first values (order of magnitude 10^6, 10^5) has a much greater impact on the calculation of the total error than the deviation from the last values (10, 1). Therefore, the solution (see the file I posted) is almost exclusively just the connection of the first two data points and the rest is virtually ignored.

EDIT:

Here is a way to get a pretty good fit using the original data and a power function. The method is to minimize the relative error instead of the absolute error(s) which genfit, line and the other fit methods do.

The outcome is (function f5) is a bit different from the result of the linear regression of the log data (Function f2) and on optical inspection I would say that f2 still is the better fit. But you have to decide which fit better your specific needs.