Solve for 'x':
3^2x - 8.3^x - 9 = 0
$\displaystyle 3^{2x} - 8 \times 3^x - 9 = 0 \Rightarrow (3^x)^2 - 8 (3^x) - 9 = 0 \Rightarrow w^2 - 8w - 9 = 0$ where $\displaystyle w = 3^x$.
After a bit more working:
Therefore $\displaystyle 3^x = 9 = 3^2$ or $\displaystyle 3^x = -1$.
One of these has no real solutions. The other has one real solution.
Therefore x = ......