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If x and y are positive real numbers s...

If x and y are positive real numbers such that ` 2log(2y - 3x) = log x + log y," then find the value of " x/y`.

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Verified by Experts

The correct Answer is:
`4/9`
We have ` 2log(2y - 3x)= log x + log y`
` rArr log(2y-3x)^(2) = log xy`
` rArr 4y^(2) - 12xy + 9x^(2) = xy`
`rArr 4y^(2) - 13xy + 9x^(2) = 0`
` rArr (4y-9x)(x-y) = 0`
` rArr 4y = 9x ` (As for x = y , LHS is not defined)
` rArr x/y = 4/9`
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