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Question
If `log(( x - y)/4) = logsqrt(x) + log sqrt(y)`, show that (x + y)2 = 20xy
Solution
`log(( x - y)/4) = logsqrt(x) + log sqrt(y)`
∴ `log((x - y)/4) = log(sqrt(x) sqrt(y))` ...[log m + log n = log mn]
∴ `log((x - y)/4) = logsqrt(xy)`
∴ `(x - y)/4 = sqrt(xy)`
Squaring on both sides, we get
`(x - y)^2/16` = xy
∴ x2 – 2xy + y2 = 16xy
Adding 4xy on both sides, we get
x2 + 2xy + y2 = 20xy
∴ (x + y)2 = 20xy
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