This isn't correct.
Try letting $u=3^x$ and see what you come up with.
Solve $3^{2x} - 3^{x+2} + 8 = 0$ for $x$.
I tried:
${\log_{e} 3^{2x}} - {\log_{e} 3^{x+2}} + {\log_{e} 8} = 0$
$\displaystyle{\frac{\log_{e} 3^{2x}}{\log_{e} 3^{x+2}}} + {\log_{e} 8} = 0$
${\log_{e} 3^{x - 2}} + {\log_{e} 8} = 0$
$x = -\displaystyle{\frac{\log_{e} 8}{\log_{e} 3}} + 2$