Question

x+y= 47xy show that log(x+y)= 1/2[ log x+log y+2log7]​

Answer 1

Answer:

Originally Answered: If log (x+y/7)=1/2(log x+log y) then what is the proof of x/y+y/x=47?

log((x+y)/7)=1/2(logx+logy)  

log((x+y)/7)=1/2(log(xy))  

log((x+y)/7)=1/2(log(xy))  

log((x+y)/7)=log(sqrt(xy))  

(x+y)/7)=sqrt(xy)  

Squaring on Both Sides,

(x+y)2=49xy  

x2+y2+2xy=49xy  

x2+y2=47xy  

(x2+y2)/xy=47  

x/y+y/x=47  

Hence Proved!