Có bao nhiêu số nguyên $x$ thỏa mãn $\left[ \log _{2}^{2}\left( 4x...

Điều kiện: $x>0; {{3}^{x}}-{{3.2}^{x-1}}\ge 0$
TH1: ${{3}^{x}}-{{3.2}^{x-1}}=0\Leftrightarrow {{3}^{x}}=\dfrac{3}{2}{{.2}^{x}}\Leftrightarrow {{\left( \dfrac{3}{2} \right)}^{x}}=\dfrac{3}{2}\Leftrightarrow x=1(t/m)$
TH2: $\left\{ \begin{matrix}
{{3}^{x}}-{{3.2}^{x-1}}>0 \\
\log _{2}^{2}\left( 4x \right)-3{{\log }_{\sqrt{2}}}x-7\le 0 \\
\end{matrix} \right.\Leftrightarrow \left\{ \begin{matrix}
x>1 \\
{{\left( 2+{{\log }_{2}}x \right)}^{2}}-6{{\log }_{2}}x-7\le 0 \\
\end{matrix}\Leftrightarrow \left\{ \begin{matrix}
x>1 \\
\log _{2}^{2}x-2{{\log }_{2}}x-3\le 0 \\
\end{matrix} \right. \right.$
$\Leftrightarrow \left\{ \begin{matrix}
x>1 \\
-1\le {{\log }_{2}}x\le 3 \\
\end{matrix}\Leftrightarrow \left\{ \begin{matrix}
x>1 \\
\dfrac{1}{2}\le x\le 8 \\
\end{matrix}\Leftrightarrow 1<x\le 8 \right. \right.$
$\Rightarrow x\in \left\{ 1;2;3;...;8 \right\}$