I have data points - denoted in the Plot by $F_k$ - covering quite a large range ($1$ - $10^{1010}$). I Plotted them in a ListLogPlot. Then I tried to fit these data points using nonlinearModelFit and now I have two problems:

1. Fitting the data points with the model: fit = NonlinearModelFit[Fk[300], $ak^{Bk}$, {a, B}, k] gives the Output: FittetModel: $1k^1$. Fitting the data points however with: fit2 = NonlinearModelFit[Fk[300], $ak^{(b*c)k}$, {a, b,c}, k] gives the Output: 140.714 $k^{1.16997 k}$ which I completely do not unterstand. I mean why should the output change upon inserting the variable $c$, which could also be combined with $b$ sucht that say $bc= B$ and 'fit' should be equal to 'fit2'.

2. If I now want to plot the data- $F_k$ vs. $k$- together with the fitted model the fitted curve ends at some value of k$\approx$ 120, and I do not unterstand why: My code for this is just: Show[{ListLogPlot[Fk[300], PlotStyle -> Red], LogPlot[fit2[k],{k,0,300}]}]