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The value of x for which the sixth term ...

The value of x for which the sixth term in the expansion of
`[2^(log_(2)sqrt(9^(x-1)+7))+(1)/(2^(1/5log_(2)(3^(x-1)+1)))]^(7)` is 84 is

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
C, D
`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`
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CENGAGE PUBLICATION-BINOMIAL THEOREM-Multiple Correct Answer Type
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