This was one of the previous year's exam questions. I have to order the following functions according to their growth rates using the $\mathcal O(n)$ notation.
$f_1(n) = 2010 * \log_3(n^n)$
$f_2(n) = n^{1+2+...+ \log_2 \log_2 n }$
$f_3(n) = 4^{100+\log_2 n}$
How do I deal with these kind of problems?