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Question
Answer the following:
If `log ((x - y)/5) = 1/2 logx + 1/2 log y`, show that x2 + y2 = 27xy
Solution
`log ((x - y)/5) = 1/2 logx + 1/2 log y`
Multiplying throughout by 2, we get
`2log ((x - y)/5)` = log x + log y
∴ `log((x - y)/5)^2` = log xy
∴ `(x - y)^2/25` = xy
∴ x2 – 2xy + y2 = 25xy
∴ x2 + y2 = 27xy
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