SOLUTION: If {{{ log ((a+b)/2) = (log a + log b) 1/2 }}} show that a=b

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Question 478102: If
+log+%28%28a%2Bb%29%2F2%29+=++%28log+a+%2B+log++b%29+1%2F2+
show that a=b
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28a%2Bb%29%2F2%29+=+%28loga+%2Blogb%29%2F2
==> log%28%28a%2Bb%29%2F2%29+=+log%28sqrt%28ab%29%29
==> %28a%2Bb%29%2F2+=+sqrt%28ab%29, since log is 1-to-1
==> %28a%2Bb%29+=+2sqrt%28ab%29
==> %28a%2Bb%29%5E2+=+4ab, after squaring both sides.
==> a%5E2+%2B+2ab+%2B+b%5E2+=+4ab
==> a%5E2+-+2ab+%2B+b%5E2+=+0
==> %28a-b%29%5E2+=+0 ==> a - b = 0, or a = b.