\[\boxed{\mathbf{13.}}\]
\[3^{x^{2} - 2x + a} = 9^{x}\]
\[3^{x^{2} - 2x + a} = \left( 3^{2} \right)^{x}\]
\[3^{x^{2} - 2x + a} = 3^{2x}\]
\[x^{2} - 2x + a = 2x\]
\[x^{2} - 4x + a = 0\]
\[D = 16 - 4a\]
\[Уравнение\ имеет\ единственный\ \]
\[корень\ при\ D = 0:\]
\[16 - 4a = 0\]
\[- 4a = - 16\]
\[a = 4.\]
\[Ответ:при\ a = 4.\]