Question 701297: I think this is the right section..
Solve 9^n –(6 × 3^n)– 27 = 0 and explain why it has only one real solution.
Hint: let 3^n = x
Can someone please solve this for me?
Thank you
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If 3^n = x , then x^2 = (3^n)^2 which means x^2 = (3^2)^n and that x^2 = 9^n
So
9^n –(6 × 3^n)– 27 = 0
would turn into
x^2 - 6x - 27 = 0
This has at most 2 solutions. It turns out that the two solutions are x = 9 or x = -3
However, since x = 3^n and 3^n is always positive (for any value of n), saying x = -3 or 3^n = -3 is impossible because there are no values of n that satisfy that equation.
So there is only one solution, namely x = 9. Since x = 3^n, the solution for n is n = 2
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