So since the numerator is undefined as we approach 1 from the left, the entire function is undefined there, and so the limit does not exist for that reason.
Now, does exist. That should be fun for you to find (but not that difficult--honest)
I am not sure if this make sense. now I know that as x approchase 1 from the right ln(x)= negitive infinity.. so as x approchase to 1 from the right ln(ln(x))/ln(x)= ln(negitive infinity)/negitive infinity.. so now the numerator undifined and the denominator equal to negitive infinity
This all I know