Question 701297
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