\(\Leftrightarrow\left(log_3x+2\right)^2-\left(m+5\right)log_3x+3m-10=0\)
Đặt \(log_3x=t\in\left[0;4\right]\)
\(\Rightarrow\left(t+2\right)^2-\left(m+5\right)t+3m-10=0\)
\(\Leftrightarrow t^2-\left(m+1\right)t+3m-6=0\)
\(\Leftrightarrow t^2-t-6-m\left(t-3\right)=0\)
\(\Leftrightarrow\left(t-3\right)\left(t+2\right)-m\left(t-3\right)=0\)
\(\Leftrightarrow\left(t-3\right)\left(t+2-m\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}t=3\\t=m-2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}m-2\ne3\\0\le m-2\le4\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}m\ne5\\2\le m\le6\end{matrix}\right.\)