If (8^{x} ÷ (frac{1}{4})^{y} = 1) and (log_{2}(x – 2y) = 1), find the value of (x – y).
-
A.
(frac{5}{4}) -
B.
(frac{3}{5}) -
C.
(1) -
D.
(frac{2}{3})
Correct Answer: Option A
Explanation
(8^{x} ÷ (frac{1}{4})^{y} = 1)
((2^{3})^{x} ÷ (2^{-2})^{y} = 2^{0})
(2^{3x – (-2y)} = 2^{0})
(implies 3x + 2y = 0 …. (1))
(log_{2}(x – 2y) = 1)
( x – 2y = 2^{1} = 2 ….. (2))
Solving equations 1 and 2,
(x = frac{1}{2}, y = frac{-3}{4})
((x – y) = frac{1}{2} – frac{-3}{4} = frac{5}{4})