Solve $3^{2x} - 3^{x+2} + 8 = 0$ for $x$.

I tried:

${\log_{e} 3^{2x}} - {\log_{e} 3^{x+2}} + {\log_{e} 8} = 0$

$\displaystyle{\frac{\log_{e} 3^{2x}}{\log_{e} 3^{x+2}}} + {\log_{e} 8} = 0$

${\log_{e} 3^{x - 2}} + {\log_{e} 8} = 0$

$x = -\displaystyle{\frac{\log_{e} 8}{\log_{e} 3}} + 2$