If $8^{x} = 2$ and $3^{x + y} = 81$ , then $y$ is equal to:

\frac{1}{3}

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\frac{9}{3}

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\frac{11}{3}

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\frac{13}{3}

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4

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Solution

The correct option is C $\frac{11}{3}$
We have $8^{x} = 2 \Rightarrow 2^{3 x} = 2$
$∴ x = \frac{1}{3}$

Also, $3^{(x + y)} = 3^{4}$
$∴ x + y = 4$
$∴ y = 4 - \frac{1}{3} = \frac{11}{3}$

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