If (2x)(2y) = 8 and (9x)(3y) = 81, then (x, y) is:

Answer: Option A

2^x. 2^y = 8
⇒ 2^{x + y} = 2³
On comparing both sides
x + y = 3 . . . . . . . (i)
Also,
9^x. 3^y = 81
⇒ 3^2x. 3^y = 3⁴
⇒ 3^{2x + y} = 3⁴
On comparing both sides
2x + y = 4 . . . . . . . (ii)
On solving equation (i) and (ii)
x = 1
y = 2
∴ (x, y) = (1, 2)