Số nghiệm nguyên của bất phương trình $\left( x-1 \right).ln\left(...

Ta có $\left( x-1 \right).\ln \left( 5-x \right)>0\Leftrightarrow \left[ \begin{aligned}
& \left\{ \begin{aligned}
& x-1>0 \\
& \ln \left( 5-x \right)>0 \\
\end{aligned} \right. \\
& \left\{ \begin{aligned}
& x-1<0 \\
& \ln \left( 5-x \right)<0 \\
\end{aligned} \right. \\
\end{aligned} \right.$
$\Leftrightarrow \left[ \begin{aligned}
& \left\{ \begin{aligned}
& x>1 \\
& 5-x>1 \\
\end{aligned} \right. \\
& \left\{ \begin{aligned}
& x<1 \\
& 0<5-x<1 \\
\end{aligned} \right. \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x>1 \\
& x<4 \\
\end{aligned} \right.\Leftrightarrow 1<x<4\Rightarrow x=\left\{ 2; 3 \right\}$