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

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

1. (1,2)
2. (2, 1)
3. (1,1)
4. (2, 2)

Correct Option: A

2^x.2^y = 8
⇒ 2^x+y = 2³
⇒ x + y = 3 ...(i)
9^x.3^y = 34
⇒ 3^2x . 3^y = 34
⇒ 2x + y = 4 ...(ii)
By equation (ii) – (i),
x = 1
From equation (i),
1 + y = 3
⇒ y = 3 – 1 = 2
Method 2 :
You can check through options also.
⇒ y = 2
⇒ (1, 2)