(a) If $\log _{2} x=9$, then $x=$

Step 1 ：Given that \(\log _{2} x=9\), we need to find the value of x.

Step 2 ：This can be rewritten as \(x = 2^9\) according to the definition of logarithms.

Step 3 ：Calculating \(2^9\), we get x = 512.

Step 4 ：So, the final answer is \(\boxed{512}\).