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

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xetabeta | Student, Kindergarten | (Level 1) Salutatorian

Posted September 18, 2013 at 7:13 AM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 18, 2013 at 7:18 AM (Answer #1)

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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

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