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`

Answer

B

Explanation

Given , `T_6=84 rArr T_(5+1)=84 rArr .^7C_5(2^("log"_2 sqrt((9^(x-1)+7))))^2(1/(2^(1//5)log_2(3^(x-1)+1)))^5=84`
`rArr 21(sqrt((9^(x-1)+7)))^2(1/(2^(log_2(3^(x-1)+1))))=84 rArr (9^(x-1)+7)(1/(3^(x-1)+1))=4`
Put `3^(x-1)=t rArr (t^2+7)/(t+1)=4 rArr (t-1)(t-3)=0 rArr t=1,3 rArr 3^(x-1)=1,3^(x-1)=3`
`therefore` x-1=0 and x-1 =1 , `therefore` x=1,2