Question 815452
<br>
{{{x^2+y^2=7xy}}}<br>
A common "trick" for working on an equation like this, with "{{{x^2+y^2}}}" on the left and an expression involving "{{{xy}}}" on the right, is to add {{{2xy}}} on the left to make a perfect square trinomial.<br>
{{{x^2+2xy+y^2=7xy+2xy}}}<br>
{{{(x+y)^2=9xy}}}<br>
The problem asks us to find an expression for log(x+y), so take logs of both sides:<br>
{{{2log((x+y))=log((9))+log((x))+log((y))}}}
{{{2log((x+y))=2log((3))+log((x))+log((y))}}}
{{{log((x+y))=log((3))+(1/2)log((x))+(1/2)log((y))}}}
{{{log((x+y))=log((3))+(1/2)(log((x))+log((y)))}}}<br>