Have you see the graph?
Please provide definitions:
1) Domain
2) Range
3) Asymptote
It is very likely these definitions will lead you to the correct response.
ln x - Wolfram|Alpha
this might help as you can see ln(0) is
however, this is not in the domain of ln(x)
BigWave) The logarithm function decreases without bound as x approaches zero from the positive side. There is no such thing as ln(0). It is not a meaningful notation. x = 0 is NOT in the Domain of y = ln(x).
Bushy) Really?! x = -4 is NOT an asymptote, yet y = ln(x) is undefined at x = -4.
Mathematics, people! We have rules and definitions and foundations. Jargon-related discussion is likely to be more confusing than helpful.
CSG18, did you look at that graphical depiction, yet? It should answer your questions. You should still consider carefully the actual definitions of things.