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