If ${log}_{4} 2 + {log}_{4} 4 + {log}_{4} x + {log}_{4} 16 = 6$ , then value of $x$ is

64

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4

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8

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32

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Solution

The correct option is D $32$
We have ${log}_{4} 2 + {log}_{4} 4 + {log}_{4} x + {log}_{4} 16 = 6$

$\Rightarrow {log}_{4} (2 \times 4 \times x \times 16) = 6$
$\Rightarrow 128 x = 4^{6}$

$\Rightarrow 4^{3} \times 2 x = 4^{6}$

$\Rightarrow x = \frac{4^{3}}{2}$

$\Rightarrow x = 32$

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