Question

if x*2+y*2=25xy,then prove that 2log(x+y)=3log3+logx+logy

Answer 1

Step-by-step explanation:

Given that,

x^2+y^2=25xy

adding +2xy on both sides

x^2+y^2+2xy=25xy+2xy

(x+y)^2=27xy

adding log on both sides

log(x+y)^2=log27xy

2log(x+y)=log 27xy (since log a^m=m.loga)

2log(x+y)=log 27+log x+ log y ( since log (ab)=log a+logb)

2log(x+y)=log 3^3+logx +logy

2log (x+y)=3log3 +logx+logy (since log a^m=m.loga)

2log(x+y)=3log3+logx+logy

Hence proved

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