If $2 log y - log x - 3 = 0$ express $x$ in terms of $y .$

x^{2} = 1000 y

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x^{2} = \frac{y^{2}}{e^{3}}

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y^{2} = \frac{x}{1000}

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y^{2} = 1000 x

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Solution

The correct option is B $x^{2} = \frac{y^{2}}{e^{3}}$
Given: $2 log y - log x - 3 = 0$

$log y^{2} - log x - 3 log e = 0$ ....... $(log e = 1)$

$log y^{2} - log x - log e^{3} = 0$

$log x = log y^{2} - log e^{3} = log (\frac{y^{2}}{e^{3}})$

$x = \frac{y^{2}}{e^{3}}$

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