anonymous
  • anonymous
9^x - 2*3^(x+1) = 27 I know that x=2, but how can I get there?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
9^x - 2*3^(x+1) = 27 3^(2x) - 6*3^x - 27 = 0 [3^x - 9][3^x +3] = 0 so 3^x = 9 or 3^x = -3 the second one is absurd
anonymous
  • anonymous
Wow, that's incredible. I never would have thought to factor it out. Thanks so much!
anonymous
  • anonymous
you're welcome

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anonymous
  • anonymous
alternate way is by using notation. suppose 3^x = p. the equation will be p^2 -6p-27=0 (p-9) (p+3) = 0 p = 9 p = -3 remember that we suppose p =3^x, so 3^x= 9 and x =2
anonymous
  • anonymous
I'm kind of angry, as this was worth 10% of the test I just took, and we'd never done anything like this in class. I literally just spent an hour trying to figure this out before coming here. Thanks again!
anonymous
  • anonymous
you're welcome

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