$\begin{array}{l}
5)DK:\left\{ \begin{array}{l}
x > 0\\
{\log _2}x \ge - \frac{3}{5}
\end{array} \right.\\
PT \Leftrightarrow \sqrt {10{{\log }_2}x + 6} = - {\log _2}x\\
\Leftrightarrow \left\{ \begin{array}{l}
- {\log _2}x \ge 0\\
10{\log _2}x + 6 = \log _2^2x
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{\log _2}x \le 0\\
\log _2^2x - 10{\log _2}x - 6 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{\log _2}x \le 0\\
\left[ \begin{array}{l}
{\log _2}x = 5 + \sqrt {31} \left( {loai} \right)\\
{\log _2}x = 5 - \sqrt {31}
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow {\log _2}x = 5 - \sqrt {31} \left( {TMDK} \right)\\
\Leftrightarrow x = {2^{5 - \sqrt {31} }}\\
6)DK:\left\{ \begin{array}{l}
x > 0\\
\log x \ne - 2\\
\log x \ne - 4
\end{array} \right.\\
PT \Leftrightarrow \frac{{2 + \log x}}{{\left( {4 - \log x} \right)\left( {2 + \log x} \right)}} + \frac{{2\left( {4 - \log x} \right)}}{{\left( {4 - \log x} \right)\left( {2 + \log x} \right)}} = \frac{{\left( {4 - \log x} \right)\left( {2 + \log x} \right)}}{{\left( {4 - \log x} \right)\left( {2 + \log x} \right)}}\\
\Rightarrow 2 + \log x + 8 - 2\log x = 8 + 2\log x - {\log ^2}x\\
\Leftrightarrow {\log ^2}x - 3\log x + 2 = 0 \Leftrightarrow \left[ \begin{array}{l}
\log x = 1\\
\log x = 2
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 10\\
x = 100
\end{array} \right.\left( {TM} \right)
\end{array}$
