Edit: While, after cooling down, I think this comment is unnecessarily mean, I'd rather have it visible as a reference and comment on article's maths than delete it entirely.
So the relevant function is not really log(wealth). It’s more like log(wealth(wealth(startup rank)), or log(e^x^y). Does that end up being log scale? Linear? Exponential? Without knowing the specific parameters, it’s impossible to tell.
Maybe I shouldn't come on Hubski or write essays (or, frankly, write) when everything seems to try and piss me off from the very morning, but here it goes. In today's section of nothing is impossible, it just depends on precision requirements:
Log(e^x^y) = x^y * Log(e) (and Log(e) = 1 if it's a natural logarithm, which it isn't because those are distinctly marked as Ln), so the plot would actually be a 2D sheet embedded in 3D XYZ space and become a exponential function of y for x constant (f(y) = x^y) and power function at y constant (f(x) = x^y). x > 0 everywhere. When taking one variable constant, you're kinda seeing a 'slice' from that sheet I mentioned.
In case of determining specifics, it's a golden rule in modeling that you don't have to be exact ('cause you can't) but have to be good enough for the thing you model, at a range you model. In radiometry, you so rarely work with a single isotope that the actual (EDIT: but still simplified and incomplete) decay formula is A exp(-Vt) + B exp(-Wt) + however many terms, each with two parameters for each distinct isotope of a compound you work with. But it'd be borderline uninstructive for illustrating the concept, so anyone else rarely (if ever) sees it beyond "How much isotope left (time) = Starting Amount * exp(-Isotope's Halflife Constant * time)."
What you have there would be perfectly serviceable in the class of functions C^x +D, 0<C<1, C,D=constant. Or, shit, C/(x - 1). But then again, it's probably not enough for this super-duper precise empirical-by-handwaving model. After all, you're trying to use it later to do asymptotic reasoning for/with/through the arbitrary parameter of 'startup rank', and it's not important to just know the (existence of a) value at a limit because math is about the journey, not the destination. Hey, wait a second...
I actually got to nine respectable paragraphs in my proper rebuttal, but this is SSC/LR through and through. Folks introducing themselves as rationalists who disregard/flunk maths but authoritatively talk about AI and AI accessories by peppering in fifty techy analogies where a dictionary would do, but only discussing them within the bounds of their 'infohazard' trigger warnings. I'll take my time, but if I forget to finish it, this won't hurt the sum total of human knowledge beyond the fact you, the reader, are now aware of Roko's Basilisk and will be tortured for eternity in Robot Hell for not aiding your benevolent AI master come to existance sooner.
Initially, I tried to work in "your eyes say no, but you have no mouth and must scream" but failed.
 - Though his early posts seem fine for what I read.