$\log _{2} 11-\log _{2} 9=\log _{2}$

Step 1 ：\(\log _{2} 11 - \log _{2} 9 = \log _{2} x\)

Step 2 ：Using the logarithm property \(\log _{a} b - \log _{a} c = \log _{a} \frac{b}{c}\), we get:

Step 3 ：\(\log _{2} \frac{11}{9} = \log _{2} x\)

Step 4 ：\(x = \frac{11}{9}\)

Step 5 ：\(\boxed{x \approx 1.222}\)