Question

if log x+y/3=1/2(logx+logy)then find the value of x/y+y/x​

Answer 1

Answer:

x/y+y/x = 7

Step-by-step explanation:

Log x+ y /3 = 1/2(logx+logy)

2[log(x+y)/3]= log(xy) : (Property of log used)

(i) loga+ logb = log(ab)

[log(x+y)/3]² = log(xy) : property of log used

(ii) nloga = loga^n

[log(x+y)/3]² = log (xy)

remove log from both sides

• [(x+ y)/3]² = xy

• x²+y²+2xy /9 = xy

• x²+y² +2xy = 9xy

• x²+y² = 7xy

• x²/xy + y²/xy = 7

• x/y + y/x = 7 Answer