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when you plug in 4 it becomes a 0^0. So I attempted to manipulate it so it would become a 0/0 form so I could l'hopital it. (sorry if I keep spelling it wrong)

so lim(x-4)ln(3x-12)=lny

then I l'hopitaled it:

lim (x-4)(1/3x-12)*3+ln(3x-12)=lny

lim 1+ln(3x-12)=lny

lim e + (3x-12)=y

so y=e

I do not know if my logic makes sense or not. If anyone sees any flaws in my logic, I would really like to know.