Perhaps you can see how to adapt this to get the slope you want. I will try to use the same style and methods that Mr. Krause used.
Suppose I want to find that negative slope between 1000 and 8000 on his log plot. First I want to extract the points in that range.
loghist = Select[couL /@ Gather[data], 1000 <= First[#] <= 8000 &]
You should be able to see in that output it has selected only those bins.
Next, the histogram is displayed on a log scale, so we need to apply Log to each histogram height.
logbin[l_List] := {First[l], Log[Last[l]]};
logs = logbin /@ loghist
You should be able to compare that with the previous output to verify it took the log of the second item in each pair.
Next you want to fit a line to that
line = Fit[logs, {1, x}, x]
If everything worked you should see the result 5.82084 - 0.000457487 x, but remember that is in (natural) Log space.
Just as a quick check you could overlay the histogram and the line
Show[ListLogPlot[loghist], Plot[line, {x, 1000, 8000}]]
If everything worked then you should see the line neatly fit into the cloud of points.
I leave it up to you to understand how to now interpret the 5.82084 and -0.000457487