What I usually do to compare asymptotic is, I will keep taking log of all the functions, unless and until it will be easy to compare. For example think of the above problem
1) log n --> After taking log it will be --> log log n
2) (log n)^c --> after taking log it will be --> c log log n
3) SQRT(n) --> after taking log it will be --> (1/2) log n
Now you can see very clearly that (1) < (2) < (3).
The beauty of this method is that you can apply this to each and every function.