Answer:The solution is [tex]x = 0.5[/tex]Step-by-step explanation:We need to write everything as a power of 3.We know that: [tex]\sqrt{a} = a^{0.5}[/tex]So[tex]\sqrt{3} = 3^{0.5}[/tex]And[tex]9 = 3^{2}[/tex]This following property is also important:[tex]\frac{a^{b}}{a^{c}} = a^{b-c}[/tex]To solve, the first step is putting everything with the variable x on one side and everything without the variable x on the other side[tex]\sqrt{3}.3^{3x} = 9[/tex][tex]3^{0.5}.3^{3x} = 3^{2}[/tex][tex]3^{3x} = \frac{3^{2}}{3^{0.5}}[/tex][tex]3^{3x} = 3^{2-0.5}[/tex][tex]3^{3x} = 3^{1.5}[/tex]This means that:[tex]3x = 1.5[/tex][tex]x = \frac{1.5}{3}[/tex][tex]x = 0.5[/tex]