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$^{x + y}$ = 1...

If 2 $^{x + y}$ = 16 and 4 $^{x - y} = \frac{1}{32}$ , find...

If 2 $^{x + y}$ = 16 and 4 $^{x - y} = \frac{1}{32}$ , find the values of x and y.

A.

x = $\frac{3}{4}$ , y = $\frac{11}{4}$

B.

x = $\frac{3}{4}$ , y = $\frac{13}{4}$

C.

x = $\frac{2}{3}$ , y = $\frac{4}{5}$

D.

x = $\frac{2}{3}$ , y = $\frac{13}{4}$

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Correct answer is B

2 $^{x + y}$ = 16 ; 4 $^{x - y}$ = $\frac{1}{32}$ .

$\implies 2^{x + y} = 2^4$

$x + y = 4 ... (1)$

$2^{2(x - y)} = 2^{-5}$

$2^{2x - 2y} = 2^{-5}$

$\implies 2x - 2y = -5 ... (2)$

Solving the equations (1) and (2) simultaneously, we have

x = $\frac{3}{4}$ and y = $\frac{13}{4}$

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