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})
Correct Answer: Option B
Explanation
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})
There is an explanation video available below.