Question

if log(x+y/3)=1/2 ( log x + log y ) show that ( x-y )2 = 5xy​

Answer 1

Answer:

Consider both sides of given equation

2log(x+y)=log5+logx+logy

log(x+y)²=log(5xy)

Cancel log on both the sides and expand bracket square of x+y

x²+2xy+y² = 5xy

x²+y² = 3xy

x²-2xy+y² = xy

(x-y)²=xy

Take log on both sides

log(x-y)²=logxy

2log(x-y)=logxy

log(x-y)=1/2(logxy)

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

This is the proof.