Prove:
$\frac n {log_2 n} = \Omega (n^{\frac 1 {100}})$
$3^{log_a {n}} = O(3^{log_b {n}})$ where $a>b>0$
For 1 we need to show that: $\frac n {log_2 n} \ge c (n^{\frac 1 {100}})$ I don't see an easy way to do it, also taking a limit of their quotient isn't simple either, the result after just one LHR is even more complicated, so I don't know how to continue.
For 2, I'm not sure how to solve their quotient limit, so I tried:
$3^{log_a {n}} \le c (3^{log_b {n}}) \Rightarrow 3^{log_a {n}-log_b {n}} \le c \Rightarrow 3^{log_a {n}-log_a {n}/log_a {b}} \le c $ and I'm stuck again.