Tìm số nghiệm của phương trình {log_2}(x^2-3)-{log_2}(6x-10)+1=0

$\begin{array}{l} {\log _2}({x^2} - 3) - {\log _2}(6x - 10) + 1 = 0\left\{ {\begin{array}{*{20}{c}} {{x^2} - 3 > 0}\\ {6x - 10 > 0}\\ {{{\log }_2}\frac{{{x^2} - 3}}{{6x - 10}} = - 1} \end{array}} \right.\\ \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {x > \sqrt 3 }\\ {\frac{{{x^2} - 3}}{{6x - 10}} = \frac{1}{2}} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {x > \sqrt 3 }\\ {2{x^2} - 6x + 4 = 0} \end{array}} \right.\\ \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {x > \sqrt 3 }\\ {\left[ {\begin{array}{*{20}{c}} {x = 1}\\ {x = 2} \end{array}} \right.} \end{array}} \right. \Rightarrow x = 2 \end{array}$