Funny pictures of sexps

[jaydfox]

Even though it might not be explicitly obvious, I suspect the same problem is hidden in the steps you have taken.

It may be that something similar is here in play. Indeed the development at 1.5 is though solvable but inaccurate:

Well, when in doubt, test with something we know the answer for. If I recall correctly, this method can be adapted to find the Abel function of cx, namely the logarithm base c? f(x) = cx is of course entire, so it should be quite amenable to your recentering approach.

Edit: But I can imagine without performing the computations that this would probably not tell us anything, because the branches of the logarithm are identical, except for a constant difference. This is not true of the slog.