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$1$) Điều kiện : $\left\{ \begin{array}{l}
1 \ne 2 - x > 0\\
1 \ne 4 - y > 0\\
2 - y > 0\\
2x - 2 > 0
\end{array} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{
\begin{array}{l}
1 < x < 2\\
y < 2
\end{array} \right.$
$1 < x < 2\,\,\, \Rightarrow \,\,0 < 2 - x < 1\,\,$
$y < 2\,\,\,\, \Rightarrow \,\,\,4 - y > 1$ do đó :
$\begin{array}{l}
\,\,\,\,\,\,\,\left\{ \begin{array}{l}
{\log _{2 - x}}\left( {2 - y} \right) > 0\\
{\log _{4 - y}}\left( {2x - 2} \right) > 0
\end{array} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\left\{ \begin{array}{l}
0 < 2 - y < 1\\
2x - 2 > 1
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x > \frac{3}{2}\\
1 < y < 2
\end{array} \right.
\end{array}$
Vậy ĐS : $\left\{ \begin{array}{l}
\frac{3}{2} < x < 2\\
1 < y < 2
\end{array} \right.$
$2$) ĐS : $\left\{ \begin{array}{l}
1 < x < 2\\
1 < y < 2
\end{array} \right.$
$3$) ĐS: $\left\{ \begin{array}{l}
4 < x < 5\\
\frac{5}{2} < y < 3
\end{array} \right.$
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