Prove using the definition of (log2(n)) or the limit test the following theorem.

Theorem 1. Let d > 1 be a real number. logd (n) 2 is (log2(n))

2. Prove using the definition of (n) or the limit test the following theorem.

Theorem 2. Let f (n) is (n) and let g (n) is (n) then f (n)+ g (n) is (n).