Question

If x2+y2 = 6xy then show that 2logx+y =logs +logs +3log2

Answer 1

Given, x² + y² = 6xy


= > x² + y² = 8xy - 2xy


= > x² + y² + 2xy = 8xy -------: ( 1 )




Then,


To prove : 2 log ( x + y ) = log x + log y + 3 log 2




$\bold{Proof : }$

LHS = >

= > 2 log ( x + y )


By the properties of logarithms


= > log ( x + y )²

= > log { ( x )² + ( y )² + 2xy }

= > log { x² + y² + 2xy }


From ( i ),


= > log { 8xy }


From the properties of logarithms


= > log 8 + log x + log y


= > log 2³ + log x + log y


= > 3 log 2 + log x + log y


= > log x + log y + 3 log 2



=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=


RHS = >

= > log x + log y + 3 log 2







LHS = RHS



$Hence, Proved.$