Home
Class 12
MATHS
the value of x , for which the 6th term ...

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`

Text Solution

Verified by Experts

The correct Answer is:
B
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
Promotional Banner

Similar Questions

Explore conceptually related problems

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

The value of x for which the sixth term in the expansion of [2^(log)_2sqrt(9^((x-1)+7))+1/(2^1/5(log)_2(3^((x-1)+1)))]^7 is 84 is 4 b. 1or2 c. 0or1 d. 3

For what value of x is the ninth term in the expansion of (3^(log_(3)sqrt(25^(x-1))+7)+3^(-(1)/(8)log_(3)(5^(x-1)+1)))^(10) is equal to 180

A possible value of 'x', for which the ninth term in the expansion of { 3 ^(log _(3) sqrt(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

The largest value of x for which the fourth tem in the expansion (5((2)/(5))(log)_(5)sqrt(4^(x)+44)+(1)/(5^(log_(5))(2^((x-1)+7))^((1)/(3))))^(8) is 336 is.