Solve the simultaneous equations : (log_{2} x – log_{2} y = 2 ; log_{2} (x – 2y) = 3)
Explanation
(log_{2} x – log_{2} y = 2 implies log_{2} (frac{x}{y}) = 2 )
(frac{x}{y} = 2^{2} = 4 implies x = 4y … (1))
(log_{2} (x – 2y) = 3 implies x – 2y = 2^{3} = 8 … (2))
Putting (1) into (2),
(4y – 2y = 8 implies 2y = 8)
(y = 4)
(x = 4y implies x = 4(4) = 16)
(x = 16 ; y = 4)