SOLUTION: If log (x+y)/2 = 1/2 (log x + log y) prove that x = y

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Question 1119109: If log (x+y)/2 = 1/2 (log x + log y) prove that x = y
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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If log (x+y)/2 = 1/2 (log x + log y), then


%28x%2By%29%2F2 = sqrt%28xy%29  ====>


x + y = 2%2Asqrt%28xy%29    ====>  square both sides  ====>


x2+%2B+2xy+%2B+y%5E2 = 4xy


x%5E2+-+2xy+%2B+y%5E2 = 0  ====>


%28x-y%29%5E2 = 0  ====>   x = y.

Proved ans solved.

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Notice:   The given condition is equivalent to %28x%2By%29%2F2 = sqrt%28xy%29,

                and it is  VERY  WELL  KNOWN  FACT  that the last equality is equivalent to  x = y.

                My solution gives you the proof of this fact.