$\displaystyle{ 3^{x-11} = \frac{1}{9} }$ 

 $\displaystyle{ 3^{x-11} = \frac{1}{3^2} }$ 

 $\displaystyle{ 3^{x-11} = 3^{2 *(-1)} }$ 

 $\displaystyle{ x-11 = -2 }$ 

 $\displaystyle{ x = 11-2 }$ 

 $\displaystyle{x = 9}$