Solve the following: 3^x + 9^x = 12

### 1 Answer | Add Yours

The equation `3^x + 9^x = 12` has to be solved for x.

`3^x + 9^x = 12`

=> `3^x + (3^2)^x = 12`

=> `3^x + (3^x)^2 = 12`

Let `3^x = t`

=> `t + t^2 = 12`

=> `t^2 + t - 12 = 0`

=> `t^2 + 4t - 3t - 12 = 0`

=> `t(t + 4) - 3(t + 4) = 0`

=> `(t - 3)(t + 4) = 0`

=> t = 3 and t = -4

As `t = 3^x` , and it is not possible for the power of 3 to be a negative number, the root t = -4 can be eliminated.

`3^x = 3`

=> x = 1

**The solution of the equation is x = 1**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes