Limits of a natural log

Question

lim x-> 2 [ln(x/e^x-1)]

Do I use direct substitution ? How do I do the next step after that?

Answer 1

If you use log rules, ln(x/(e^x-1) = ln(x) -ln(e^x-1) = ln(x)-(x-1)ln(e) = ln(x)-(x-1)(1)

which should make it easier to take the limit as x->2