Question

9^x - 2*3^(x+1) = 27

I know that x=2, but how can I get there?

Answer 1

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

Answer 2

Wow, that's incredible. I never would have thought to factor it out. Thanks so much!

Answer 3

you're welcome

Answer 4

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

Answer 5

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!

Answer 6

you're welcome