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

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

Question

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

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

anonymous · Answer

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 · Answer

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

anonymous · Answer

you're welcome

anonymous · Answer

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 · Answer

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 · Answer

you're welcome