the value of `x` , for which the 6th term in the expansions of`[2^log_2sqrt(9^((x-1)+7))+1/(2^(1/5)(log)_2(3^(r-1)+1))]i s84` , is equal to a. 4 b. 3 c. `2` d. `1`

Options

A. 4
B. 3
C. 2
D. 1

Answer

C, D

Explanation

`E = [sqrt(9^(x-1)+7) + (1)/((3^(r-1)+1)^(1//2))]^(7)`
Given, `T_(6) = 84`
`rArr .^(7)C_(5)(sqrt(9^(x-1)+7))^(7-5)((1)/((3^(x-1)+1^(1//5))))^(5) = 84`
`.^(7)C_(5)(9^(x-1)+7).(1)/((3^(x-1)+1)) = 84`
or `9^(x-1) + 7 = 4(3^(x-1)+1)`
or `3^(2x) - 12 . 3^(x) + 27 = 0`
or`(3^(x) -3)(3^(x) -9) = 0`
or `3^(x) = 3,9`
or `x = 1,2`