Bài giải

${{\log }_{3}}({{x}^{2}}-6)={{\log }_{3}}(x-2)+1$

$\Leftrightarrow {{\log }_{3}}({{x}^{2}}-6)={{\log }_{3}}3(x-2)$

$\Leftrightarrow \left\{ \begin{align}& {{x}^{2}}-6>0 \\ & x-2>0 \\ & {{x}^{2}}-6=3(x-2) \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& x<-\sqrt{6}\vee x>\sqrt{6} \\ & x>2 \\ & x=0\vee x=3 \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align}& x>\sqrt{6} \\& x=0\vee x=3 \\\end{align} \right.\Leftrightarrow x=3$

Chọn đáp án C.