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Question
Answer the following:
If `log (("a" + "b")/2) = 1/2(log"a" + log"b")`, then show that a = b
Solution
`log (("a" + "b")/2) = 1/2(log"a" + log"b")`
∴ `2 log (("a" + "b")/2)` = log a + log b
∴ `log (("a" + "b")/2)^2` = log ab
∴ `("a" + "b")^2/4` = ab
∴ a2 + 2ab + b2 = 4ab
∴ a2 + 2ab – 4ab + b2 = 0
∴ a2 – 2ab + b2 = 0
∴ (a – b)2 = 0
∴ a – b = 0
∴ a = b
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