Có bao nhiêu số nguyên âm $x$ thoả mãn $\left[ {{\log...

Ta có:
$\left[ {{\log }_{8}}(4-2x)-2 \right]\sqrt{-{{4}^{x-1}}+{{2}^{x-2}}+3}<0\Leftrightarrow \left\{ \begin{aligned}
& 4-2x>0 \\
& -{{4}^{x-1}}+{{2}^{x-2}}+3>0 \\
& {{\log }_{8}}(4-2x)-2<0 \\
\end{aligned} \right.$$\Leftrightarrow \left\{ \begin{aligned}
& x<2 \\
& -\dfrac{3}{4}<{{2}^{x-2}}<1 \\
& {{\log }_{8}}(4-2x)<2 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x<2 \\
& x-2<0 \\
& 4-2x<64 \\
\end{aligned} \right.\Leftrightarrow -30<x<2x$ thoả mãn.