[Highschool - Math] Having troubles Solving Exponential Equations

[og4lif]

Hello. I'm having difficulties solving this particular Exponential Equation and according to my understanding it involves logarithms.

3^2x - 6(3^x) + 9 = 0

I'm not interested in the answer. I already know that the answer is one but I am having difficulties manipulating this equation. I would really appreciate it if someone could show me what I should do because I have lots of homework with similar questions.

Below I have provided some work I attempted on this question.

3^2x - 6(3^x) + 9

log 3^2x - [log 6 + log 3^x] = - log 9

2x log 3 - log 3^x = log 6 - log 9

x[log 3^2 - log 3] = log 6/9

Eventually, If i continue I end up with the wrong answer.