Slog(e4)

[Catullus]

For \(x>\eta\), how can \(\text{slog}_x(e_4)\) be approximated in a way that becomes better and better the closer x goes to eta? What about approximating \(\text{slog}_x(e)\)? What about approximating the third real fixed point a of \(x\uparrow\uparrow a\)? What about approximating\(\lim_{k\to\infty}\text{slog}_x(k)-\text{slog}_{e_4}(k)\)?