Question

Solve the following exponential equation:
9ˣ² - 3ˣ⁺¹ = 0

Answer 1

`9^(x^2)} - 3^(x + 1) =0`

• Set up

`3^(2 x^2) - 3^(x + 1) = 0`

• Simplify 9 using the fact that
  `9 = 3^2`

`3^(2 x^2) = 3^(x + 1)`

• Add
  `3^(x + 1)` to both sides of the equation

`2 x^2 \log 3 = (x + 1) \log 3`

• Take the
  `\log` of both sides

`2 x^2 = x + 1`

• Divide both sides by
  `\log 3`

`2 x^2 - x - 1 = 0`

• Subtract
  `x + 1` from both sides of the equations to create a quadratic equation equaling 0

`(2x + 1)(x - 1) = 0`

• Factor

`2x + 1 = 0 \,\,\textrm{and} \,\, x - 1 = 0`

• Apply the Zero Product Property

`x = - (1)/(2), 1`

Our solutions are x = -1/2 and x = 1.