Ta có:

$\left\{ \begin{align}  & x={{\log }_{3}}15={{\log }_{3}}(3.5)={{\log }_{3}}5+1\Rightarrow {{\log }_{3}}5=x-1 \\  & y={{\log }_{3}}10={{\log }_{3}}(2.5)={{\log }_{3}}2+{{\log }_{3}}5\Rightarrow {{\log }_{3}}2=y-{{\log }_{3}}5=y-x+1 \\ \end{align} \right.$

Vậy:  ${{\log }_{\sqrt{3}}}50=2{{\log }_{3}}({{5}^{2}}.2)=4{{\log }_{3}}5+2{{\log }_{3}}2=4(x-1)+2(y-x+1)=2x+2y-2$