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 a. `4` b. `1or2` c. `0or1` d. `3`

Options

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

Explanation

To solve the problem, we need to find the value of \( x \) for which the sixth term in the expansion of

\[ \left[ 2^{\log_2 \sqrt{9^{(x-1)} + 7}} + \frac{1}{2^{1/5} \log_2(3^{(x-1)+1})} \right]^7 \]

is equal to 84.

...