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If 2^y = 4^(5x + 3) and 3^(x - 7) = 9^y, what is the value of x + y ?
A. -10
B. -5
C. -4
D. 3
E. 7
A. -10
B. -5
C. -4
D. 3
E. 7
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30 Nov 2014, 05:58
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FTS185
\(2^y = 4^{(5x + 3)}\) --> \(2^y = 2^{2(5x + 3)}\) --> \(y = 2(5x + 3)\);
\(3^{(x - 7)} = 9^y\) --> \(3^{(x - 7)} = 3^{2y}\) --> \(x-7=2y\).
From above \(x = -1\) and \(y=-4\) --> \(x +y = -5\).
Answer: B.
30 Nov 2014, 06:22
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2^y = 4^(5x + 3)
2^y=2^2(5x+3)
y=10x+6 ........... 1
3^(x - 7) = 9^y
3^(x-7)=3^2y
x-7=2y ............. 2
put value of y=10x+6 in eq 2
x-7=2(10x+6)
x-7=20x+12
19x=-19
x=-1
therefore, y= -10+6
y=-4
x+y= -1-4= -5
Ans - B
2^y=2^2(5x+3)
y=10x+6 ........... 1
3^(x - 7) = 9^y
3^(x-7)=3^2y
x-7=2y ............. 2
put value of y=10x+6 in eq 2
x-7=2(10x+6)
x-7=20x+12
19x=-19
x=-1
therefore, y= -10+6
y=-4
x+y= -1-4= -5
Ans - B
