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If xa n dy are real numbers such that 2...

If `xa n dy` are real numbers such that `2log(2y-3x)=logx+logy` ,then find `x/y`.

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`2log(2y-3x)=logx+logy`
`log(2y-3x)^2=logxy`
`(2y-3x)^2=xy`
`y^2[2-3x/y]^2=xy`
`4+9(x/y)^2-12x/y=x/y`
Let `x/y=t`
`4+9t^2-12t-t=0`
`9t^2-13t+4=0`
...
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