Express \(p\) in terms of \(q\) if \(\log _{4} p+2 \log _{4} \rho^{-4}-446 / {q}^{2}\)
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Correct Answer: Option A
Explanation:
\begin{aligned}
&\log _{4} p+2 \log _{4} q=4 \\
&\log _{4} p+\log _{4} q^{2}=4 \\
&\log _{4} p q^{2}=4 \\
&\Rightarrow p q^{2}=4^{4} \\
&==4^{4} / q^{2}=\left(4^{2} / q\right)=(16 / q)^{2}
\end{aligned}
\begin{aligned}
&\log _{4} p+2 \log _{4} q=4 \\
&\log _{4} p+\log _{4} q^{2}=4 \\
&\log _{4} p q^{2}=4 \\
&\Rightarrow p q^{2}=4^{4} \\
&==4^{4} / q^{2}=\left(4^{2} / q\right)=(16 / q)^{2}
\end{aligned}