Respuesta :
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]
