If you’re looking for intuition on how to notice the approach in the other comment, notice that you can rewrite the terms with a bit of algebra:

(ln n)^ln(n) = (e^ln(ln(n)) )^ln(n) = e^ln(ln(n))•ln(n) = (e^ln(n) )^ln(ln(n)) = n^ln(ln(n))

So pick n large enough so that ln(ln(n))>2