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If $\log _{4} 2+\log _{4} 4+\log _{4} x+\log _{4} 16=6$, then the value of $x$ is
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The correct answer is:
32
$\because \log _{4} 2+\log _{4} 4+\log _{4} x+\log _{4} 16=6$
$\Rightarrow \log _{4}(2 \times 4 \times x \times 16)=6$
$\Rightarrow \quad 128 x=4^{6}$
$\therefore \quad x=\frac{4^{3}}{2}=32$
$\Rightarrow \log _{4}(2 \times 4 \times x \times 16)=6$
$\Rightarrow \quad 128 x=4^{6}$
$\therefore \quad x=\frac{4^{3}}{2}=32$
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