If a 1 , a 2 , . . . , a 9 are in G . P . , then log a 1 log a 2 log a 3 log a 4 log a 5 log a 6 log a 7 log a 8 log a 9 is equal to

Step-by-step solution

Given a 1 ,   a 2 ,   a 3 , . . . ,   a 9 are in G . P . , hence, by the definition of G . P . , we have a 2 a 1 = a 3 a 2 = a 4 a 3 = . . . a 9 a 8 = r , where r is the common ratio of the G . P . Now, let △ = log a 1 log a 2 log a 3 log a 4 log a 5 log a 6 log a 7 log a 8 log a 9 Applying C 2 → C 2 − C 1 ,   C 3 → C 3 − C 2 , we get △ = log a 1 log a 2 − log a 1 log a 3 − log a 2 log a 4 log a 5 − log a 4 log a 6 − log a 5 log a 7 log