Please solve the question completely and according to given conditions in question above

Suppose that you are given a number of objects. All the objects have the same weight, with the exception of one, called the unique object, which has a different weight. In all other aspects, the objects are identical. You are required to determine which is the unique object. For this purpose, a pair of scales is provided (which allows you to compare, for any two object or two groups of objects, which is the lighter and which is the heavier). Suppose the total number of objects is 3"(n > 1). Show by induction on n that at most 2n comparisons are needed to identify the unique object. In your solution you should: 1. State explicitly what is the base case and how to solve it. (Hint: when n = 1 there are 31 = 3 objects and you need to show how to use at most 2 x 1 = 2 comparisons to identify the unique object). 2. State explicitly what is the induction hypothesis and show how to use the induction hypothesis to solve the problem (Hint: for the induction step, 3n+1 objects can be split into three groups of 3" objects)