if 3x + y = 81 and 81x - y = 3, then what is the value

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if 3^{x + y} = 81 and 81^{x - y} = 3, then what is the value of x ?

1. 17/16
2. 17/8
3. 17/4
4. 15/4

Correct Option: B

Given, 3^{x + y} = 81
⇒ 3^{x + y} = 3⁴
⇒ x + y = 4 ...(i)
and 81^{x - y} = 3 or (3⁴)^{x - y} = 3
⇒ x - y = 1/4
On solving the Eqs. (i) and (ii), we get
2x = 17/4 ⇒ x = 17/8