$$f(x)=6^{3x+9}-2.$$
I got to one step, but I became lost. I understand that I'm converting it into logarithmic form, but I don't understand what the next steps are.
\begin{align*} f(x)&=6^{3x+9}-2 \\ x&=6^{3y+9} -2 \\ x+2&=6^{3y+9} \ldots \end{align*}
Now take the base $6$ log (or the natural log) of both sides, getting $3y+9=\log_6(x+2)$ and keep working.