0\\ 2x-3>0 \end{cases}\\ \begin{cases} 3x^2-10x+3=0\\ x>\frac32 \end{cases}\\ \begin{cases} \left[\begin{array}{l} x=3\\ x=\frac13 \end{array}\right.\\ x>\frac32 \end{cases}\\ \boxed{x=3}" alt=" \lg(3x-8)+\lg x=\lg(2x-3)\\ \begin{cases} x(3x-8)=2x-3\\ x>0\\ 2x-3>0 \end{cases}\\ \begin{cases} 3x^2-10x+3=0\\ x>\frac32 \end{cases}\\ \begin{cases} \left[\begin{array}{l} x=3\\ x=\frac13 \end{array}\right.\\ x>\frac32 \end{cases}\\ \boxed{x=3}" align="absmiddle" class="latex-formula">