Question

Hope everyone can help me I'll really need your help

Answer 1

See below. The solutions are x=-1/3 and y=-4/3

Explanation:

`(1)/(2)\log_2 y-\log_4 x = 1\\(1)/(2)\log_2 y = \log_4 x+1=\log_4x+\log_4 4=\log_4 4x\\(1)/(2)\log_2y = log_44x\\(1)/(2)(\log_4y)/(\log_4 2)=\log_4 4x\\\log_4y=\log_44x\\4^(\log_4y)=4^(\log_44x)\\y = 4x\\\\x-y = 1\\4x -y = 0\\\rightarrow\\3x=-1\implies x = -(1)/(3), y=-(4)/(3)`