If $2 x^{{l o g_{4}}^{3}} + 3^{{log}_{4} x} = 27$ , then x is equal to?

2

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4

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8

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16

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Solution

The correct option is C $16$
Since, $2 x^{{l o g}_{4} 3} + 3^{{l o g}_{4} x} = 27$
$⟹ {2 \times 3}^{{l o g}_{4} x} + 3^{{l o g}_{4} x} = 27$
Let $3^{{l o g}_{4} x} = t$
$∴ 2 t + t = 27$
$⟹ 3 t = 27$
$⟹ t = 9$
Thus, $3^{{l o g}_{4}^{x}} = 9$
$⟹ 3^{{l o g}_{4}^{x}} = 3^{2}$
$⟹ {l o g}_{4} x = 2$
$⟹ x = 2^{4} = 16$ .

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