SOLUTION: Suppose that x and y are real numbers such that 4^x / 2^x+y = 8 and 9^x+y / 3^5y = 243 Which of the following is equal to xy? (a) -1 b 12/5 c 4 d 6 e 12

Question 252367: Suppose that x and y are real numbers such that 4^x / 2^x+y = 8 and
9^x+y / 3^5y = 243 Which of the following is equal to xy?
(a) -1 b 12/5 c 4 d 6 e 12

Answer by palanisamy(496) (Show Source): You can put this solution on YOUR website!
Given, 4^x / 2^x+y = 8
2^2x /2^x+y = 2^3
2^(2x-x-y) = 2^3
2^(x-y) = 2^3
Therefore, x-y = 3 ...(1)
Next, 9^(x+y) / 3^5y = 243
3^2(x+y)/3^5y = 3^5
3^(2x+2y-5y) = 3^5
3^(2x-3y) = 3^5
Therefore, 2x-3y = 5 ...(2)
Solving (1) and (2),
2x(1)-(2):
(2x-2y)-(2x-3y) = 6-5
y = 1

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