[tex]\begin{vmatrix}
1 & 1& 1\\
1 & 3 & 9\\
1& {a}^{2} & {a}^{2}
\end{vmatrix} = \Delta(a)[/tex]
[tex]\Delta(a) = 3 {a}^{2} + {a}^{2} + 9 - 3 - 9 {a}^{2} - {a}^{2} [/tex]
[tex]\Delta(a) = - 6 {a}^{2} + 6[/tex]
[tex]\Delta( {3}^{x} ) = - 6 \times { ({3}^{x} )}^{2} + 6[/tex]
[tex]\Delta( {3}^{x} ) = - 6 \times {3}^{2x} + 6[/tex]
[tex]\Delta( {3}^{x} ) = 0[/tex]
[tex] - 6 \times {3}^{2x} + 6 = 0 \: | \div ( - 6)[/tex]
[tex] {3}^{2x} - 1 = 0[/tex]
[tex] {3}^{2x} = 1[/tex]
[tex] = > x = 0[/tex]
