Question

if 2log(x-y)=1/2(logx+logy)then find the value of x/y+y/x

Answer 1

2  Log (x - y) = 1/2 (Log x + Log y)
=>  Log (x - y)² = 1/2 ( Log x y )
                        = Log √ (x y)
       (x - y)² = √ (x y)

x/y  + y/x
  = (x² + y²) / (x y)
  = [ (x - y)² + 2 x y ] / (x y)
  = [ √(x y) + 2 xy ] / (xy)
   =  2  +  1/√(xy)

Answer 2

2log(x-y) = 1/2 (logx+logy)
= log(x-y)² = 1/2log(xy)
= log(x-y)² = log(√xy)
= (x-y)² = √xy
= x²+y²-2xy = √xy
= (x²+y²-2xy)/xy = √xy/xy
= x/y + y/x - 2 = 1/√xy
= x/y + y/x = 2 + 1/√xy