Suppose that f(x) is O(g(x)) where f and g are increasing and unbounded functions. Show that log |f(x)| is O(log|g (x)|).

Solution:Step 1:The objective of this question is to show that log |f(x)| is O(log|g (x)|).Step 2: Big-O Notation: To show that f(x) is O(g(x)) requires that we find one pair of constants C & k, there are infinitely many pairs, But if one such pair exists.The O (pronounced big-oh) is the normal method of representing an algorithm of the upper bound. It measures the time taken by the algorithm to execute it.there are infinitely many pairs, But if one such pair exists.Such that:.