if log(a+b/2)=1/2(loga+logb) proof that a=b
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Answer:
Step-by-step explanation:
log( ( a + b )/ 2 ) = log( (ab)^0.5 )
Since logs are monotonic
(a + b) = 2 . sqrt( ab )
a + b - 2 * sqrt(a) * sqrt(b) = 0
(sqrt(a) - sqrt(b))^2 = 0
sqrt(a) - sqrt(b) = 0
Which is only possible if
a = b
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