(a) If $\log _{2} x=9$, then $x=$
So, the final answer is \(\boxed{512}\).
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 \(\boxed{512}\).