SOLUTION: if Log ((a+b)/2) = 1/2 (log a + log b), show that a = b

Question 692882: if Log ((a+b)/2) = 1/2 (log a + log b), show that a = b
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if Log ((a+b)/2) = 1/2 (log a + log b), show that a = b
log((a+b)/2) = (1/2)(log(a) + log(b))
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log[(a+b)/2] = (1/2)log(a) + (1/2)log(b)
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log[(a+b)/2] = log(a^(1/2) + log(b^(1/2))
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log((a+b)/2) = log(ab)^(1/2)
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(a+b)/2 = ab^(1/2)
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Square both sides to get:
(a+b)^2/4 = ab
a^2 + 2ab + b^2 = 4ab
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a^2 - 2ab + b^2 = 0
(a-b)^2 = 0
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a = b
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Cheers,
Stan H.
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