Let us say you have two functions : f(n) and g(n) such that f(n) = O(g(n)) Assume f(n) >= 1 and log₂g(n) >= 1 for all n

For the following statements, say whether true or false and provide proof if true or give a counter-example if it is false:

1. log₂ f(n) = O(log₂ g(n))

2. 2 ^f(n) = O(2^g(n))

3. f(n) ² = O (g(n) ²)