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

Option A:

(1,2)

Option B:

(2,1)

Option C:

(1,1)

Option D:

(2,2)

Option E:

(1,3)

Option A is the correct answer.

Given (2^x) (2^y) = 8,

2^(x+y) = 2^3

x+y = 3 (from Equation 1)

(9^x)(3^y) = 81,

3^(2x) * (3^y) = 3^4

3^(2x+y) = 3^4

So 2x+y = 4 (from Equation 2)

Solving, Equation 2 – Equation 1

We get, x = 1 and y =2

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