Prove or find a counterexample for the following. Assume that f (n) and g (n) are monotonically increasing functions that are always larger than 1. f (n) = o (g (n)) rightarrow log (f (n)) = o (log (g (n))) f (n) = O (g (n)) rightarrow log (f (n)) = O (log (g (n))) f (n) = o (g (n)) rightarrow 2^f (n) = o (2^g (n)) f (n) = O (g (n)) rightarrow 2^f (n) = O (2^g (n))