Slog(Exponential Factorial(x))

[Catullus]

EF(x) = exponential factorial(x) = x^(x-1)^(x-2)^...^3^2^1.
What happens if you do the tetration logarithm of the exponential factorial function. (I am thinking tetration logarithm base the Tetra-Euler Number.) How can the tetration logarithm of the exponential factorial function be approximated?
Slog(e4,EF(1))=0.
Slog(e4,EF(2))~.636.
Slog(e4,EF(3))~1.612.
Slog(e4,EF(4))~2.693.
Slog(e4,EF(5))~3.703.
Slog(e4,EF(6))~4.703.
Numbers worked out with the Kneser method.
I conjecture that slog(k,EF(x))-x approaches a number, as x grows larger and larger, for all real k greater than eta.