Good article, but there is one step in the reasoning that rubs me the wrong way:

> This equation might seem a little hard to solve, but at this point you might notice something funny: $equation$

> So, if F′(x)log⁡(x)=1,F′(x)log(x)=1, then

> Thus, our mystery function F(x)F(x) obeys F′(x)log⁡(x)=1.F′(x)log(x)=1. From here you deduce F′(x)=1/log⁡(x),F′(x)=1/log(x), so by integrating you get

But it does not seems that F needs to have that trait, just that 1 works in that instance. It's sufficient but not necessary. How can you tell that it is that simple solution which is the right one?