please answer below question wih detailed steps, thanks!

Prove or disprove the following statements, using the relationship among typical growth-rate functions seen in class. a) 50()()()()()n5 log n + n-is O(n- log n) c) d) e) f) nn is (n!) 0.01 ns+ 0.0000001 n-is (n*) n6 + 0.0000001 n5 is (n*) n! is (2")