81^y=9/3^y (3^4)^y=3^2/3^y=3^2 y 3^4y=3^2 y Equating the powers, we get nbsp; 4y=2 y 5y=2 y=2/5 ...

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Exponent

If 81y=9/3y, ...

Question

If $81^{y} = \frac{9}{3^{y}}$ , find y.

y = \frac{1}{2}

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y = \frac{5}{2}

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y = \frac{2}{5}

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y = \frac{1}{5}

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Solution

The correct option is C $y = \frac{2}{5}$
$81^{y} = \frac{9}{3^{y}}$
$(3^{4})^{y} = \frac{3^{2}}{3^{y}} = 3^{2 - y}$
$3^{4 y} = 3^{2 - y}$
Equating the powers, we get
$4 y = 2 - y$
$5 y = 2$
$y = \frac{2}{5}$

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