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 is A

\(8^{x} ÷ (\frac{1}{4})^{y} = 1\)

\((2^{3})^{x} ÷ (2^{-2})^{y} = 2^{0}\)

\(2^{3x - (-2y)} = 2^{0}\)

\(\implies 3x + 2y = 0 .... (1)\)

\(\log_{2}(x - 2y) = 1\)

\( x - 2y = 2^{1} = 2 ..... (2)\)

Solving equations 1 and 2,

\(x = \frac{1}{2}, y = \frac{-3}{4}\)

\((x - y) = \frac{1}{2} - \frac{-3}{4} = \frac{5}{4}\)