[tex]9^{x^2}} - 3^{x + 1} =0[/tex]
[tex]3^{2 x^2} - 3^{x + 1} = 0[/tex]
- Simplify 9 using the fact that [tex]9 = 3^2[/tex]
[tex]3^{2 x^2} = 3^{x + 1}[/tex]
- Add [tex]3^{x + 1}[/tex] to both sides of the equation
[tex]2 x^2 \log 3 = (x + 1) \log 3[/tex]
- Take the [tex]\log[/tex] of both sides
[tex]2 x^2 = x + 1[/tex]
- Divide both sides by [tex]\log 3[/tex]
[tex]2 x^2 - x - 1 = 0[/tex]
- Subtract [tex]x + 1[/tex] from both sides of the equations to create a quadratic equation equaling 0
[tex](2x + 1)(x - 1) = 0[/tex]
[tex]2x + 1 = 0 \,\,\textrm{and} \,\, x - 1 = 0[/tex]
- Apply the Zero Product Property
[tex]x = - \dfrac{1}{2}, 1[/tex]
Our solutions are x = -1/2 and x = 1.
