SOLUTION: If 2log(x+y)=logx+logy+4log2, then show that x2+y2=14xy

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If 2log(x+y)=logx+logy+4log2, then show that x2+y2=14xy       Log On


   

Question 200668: If 2log(x+y)=logx+logy+4log2, then show that x2+y2=14xy






Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start on the left side and manipulate the logs to get something a little less cluttered
+2log%28x%2By%29=logx%2Blogy%2B4log2
+log%28%28x%2By%29%5E2%29=log%28%28xy2%5E4%29%29
%28x%2By%29%5E2+=+16xy
x%5E2+%2B+2xy+%2B+y%5E2+=+16xy
x%5E2+%2B+y%5E2+=+14xy