Question

If x2+y2=7xy then show that 2log (x+y)=logx+logy+2log3

Answer 1

Answer:

7xy can be written as 9xy-2xy

:.x2+y2=9xy-2xy

x2+y2+2xy=9xy

(x+y)2=9xy

Applying log on both sides

log(x+y)2=log9xy

since,logxpowerm=mlogx

log(x+y)2=2log(x+y)

since , logabc= loga+logb+logc

log9xy=log9 +logx+log y

=2log3+logx+logy

:.2log(x+y)=logx+log y+2log3