Question

Solve for x and y; if $x>0$ and $y>0$ :
$logxy=log\frac{x}{y}+2log2=2$.

Answer 1

log xy= log x/y +2 log 2 = 2
Taking the first two
$logxy=log\frac{x}{y}+2log2$
⇒ $logx+logy=logx-logy+2log2$
⇒ $logy=-logy+2log2$
⇒ $2logy=2log2$
⇒ $y=2$
Taking first and third
$logxy=2$
⇒ $log2x=2$
⇒ $2x={10}^2=100$
⇒ $x=\frac{100}{2}=50$

x = 50, y = 2