A possible value of x , for which the ninth term in the expansion of 3 log 3 25 x - 1 + 7 + 3 - 1 8 log 3 5 x - 1 + 1 10 in the increasing powers of 3 - 1 8 log 3 5 x - 1 + 1 is equal to 180 , is :

Step-by-step solution

3 log 3 25 x - 1 + 7 + 3 - 1 8 log 3 5 x - 1 + 1 10 = 25 x - 1 + 7 + 5 x - 1 + 1 - 1 8 10 , using a n log a x = x n Using the formula of the general term in the Binomial theorem for non negative integral index, i.e., T r + 1 = C r n a n - r b r   in a + b n , we get, T 9 = T 8 + 1 = C 8 10 25 x - 1 + 7 × 5 x - 1 + 1 - 1 = 180 ⇒ 25 x - 1 + 7 5 x - 1 + 1 = 4 ⇒ t 2 + 7 t + 1 = 4 , taking t = 5 x - 1 ⇒ t 2 + 7 = 4 t + 1 ⇒ t 2 - 4 t + 3 = 0 ⇒ t - 3 t - 1 = 0 ⇒ t = 1 , 3 &#86