3. Translate the curve $y=\log _{2} x$ 1 unit in the positive direction of the $x$-axis, then 2 units in the negative direction of the $y$-axis, to obtain curve $C$. Among the following curves, which one is symmetric to $C$ with respect to the line $x+y=0$?
A. $y=2^{x+2}-1$
B. $y=-2^{x+2}-1$
C. $y=-2^{2-x}-1$
D. $y=2^{2-x}-1$
$$
\begin{array}{l}
C: y=\log _{2}(x-1)-2 \Rightarrow C^{\prime}:-x=\log _{2}(-y-1)-2 \Rightarrow \log _{2}(-y-1)=2-x \\
\Rightarrow -y-1=2^{2-x} \Rightarrow y=-2^{2-x}-1, \text { so choose } C .
\end{array}
$$