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Logarithmic Inequalities

If 2log y -...

Question

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

A

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

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B

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

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C

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

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D

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

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Solution

The correct option is A $x = \frac{y^{2}}{e^{3}}$
$\Rightarrow$ $log y^{2} - log x - log e^{3} = 0$ ....... $log e = 1$

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

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

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