Question

if log (x+y)/3 =1/2(logx +log y), then find the value ofx/y+y/x.​

Answer 1

Step-by-step explanation:

We have,

$log \frac{(x + y)}{3} = \frac{1}{2} .( log(x) + log(y) )$

$\implies2 log \frac{ (x + y) }{3} = log(xy)$

$\implies log( { (\frac{ x + y}{3}})^{2} ) = log(xy)$

$\implies {(x + y)}^{2} = 9xy$

$\implies {x}^{2} + {y}^{2} + 2xy = 9xy$

$\implies {x}^{2} + {y}^{2} = 7xy$

$\implies \frac{ {x}^{2} + {y}^{2} }{xy} = 7$

$\implies \frac{x}{y} + \frac{y}{x} = 7$