Question

log(x-y) -log5-1/2logx-1/2logy=0then x/y+y/x =

Answer 1

$log(x - y) - log(5) - \frac{1}{2} log(x) - \frac{1}{2} log(y) = 0 \\ log(x - y) - log( \sqrt{x} ) - log( \sqrt{y} ) - log(5) = 0 \\ log(x - y) - ( log( \sqrt{x} ) + log( \sqrt{y} ) ) - log(5) = 0 \\ log(x - y) - log( \sqrt{x.y} ) = log(5) \\ log( \frac{x - y}{ \sqrt{x.y} } ) = log(5) \\ \frac{x - y}{ \sqrt{x.y} } = 5 \\ \frac{x}{ \sqrt{xy} } - \frac{y}{ \sqrt{xy} } = 5 \\ \sqrt{ \frac{x}{y} } - \sqrt{ \frac{y}{x} } = 5 \\ take \: square \: both \: side \: \\ { (\sqrt{ \frac{x}{y} } - \sqrt{ \frac{y}{x} } ) }^{2} = {5 }^{2} \\ \frac{x}{y} + \frac{y}{x} - 2. \sqrt{ \frac{xy}{yx} } = 25 \\ \frac{x}{y} + \frac{y}{x} - 2 = 25 \\ \frac{x}{y} + \frac{y}{x} = 27$