document.write( "Question 815452: if x*x+y*y=7xy, prove
\n" ); document.write( "log(x+y)=1/2(logx+logy)+log3 \n" ); document.write( "
Algebra.Com's Answer #853725 by greenestamps(13292)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "\"x%5E2%2By%5E2=7xy\"

\n" ); document.write( "A common \"trick\" for working on an equation like this, with \"\"x%5E2%2By%5E2\"\" on the left and an expression involving \"\"xy\"\" on the right, is to add \"2xy\" on the left to make a perfect square trinomial.

\n" ); document.write( "\"x%5E2%2B2xy%2By%5E2=7xy%2B2xy\"

\n" ); document.write( "\"%28x%2By%29%5E2=9xy\"

\n" ); document.write( "The problem asks us to find an expression for log(x+y), so take logs of both sides:

\n" ); document.write( "\"2log%28%28x%2By%29%29=log%28%289%29%29%2Blog%28%28x%29%29%2Blog%28%28y%29%29\"
\n" ); document.write( "\"2log%28%28x%2By%29%29=2log%28%283%29%29%2Blog%28%28x%29%29%2Blog%28%28y%29%29\"
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\n" ); document.write( "\"log%28%28x%2By%29%29=log%28%283%29%29%2B%281%2F2%29%28log%28%28x%29%29%2Blog%28%28y%29%29%29\"

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