Master theorem with $T(n) = 6T(n/10) + \lg^2 n$
Yuval Filmus pretty much showed the way in the comment above. I will just elaborate on his approach. 

First, we raise both to the power lg610.

(nlg106)lg610 = n(lg106 x lg610) = n

and,

(lg2n)lg610 = (lg n)2 x lg610 = (lg n)2.57

Now, taking log of both of these, we get 
lg(n) and 2.57xlg(lg(n)) respectively.

lg(n) is asymptotically greater than lg(lg(n)), and thus, our case is proved.