awkを使えばとても簡単です。以下の例を参照してください。
kent$ cat log.txt
213.64.237.213 - - [20/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [20/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [20/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [20/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [20/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [23/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [23/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [23/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.132.36.66 - - [28/Dec/2002:19:33:29 +0100]
kent$ sd=21/Dec/2002
kent$ awk -F'[:[]' -v d=$sd '$2>d' log.txt
出力
213.64.237.213 - - [23/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [23/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [23/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.64.237.213 - - [25/Dec/2002:03:02:22 +0100]
213.132.36.66 - - [28/Dec/2002:19:33:29 +0100]
アップデート
この awk 行を試してください: $sd は変数です。それがあなたのために働くことを願っています。
kent$ awk -F'[:[]' -v vd=$sd 'BEGIN{ gsub(/\//," ",vd);"date +%s -d \""vd"\""|getline d} {p=$0; gsub(/\//," ",$2); "date +%s -d \""$2"\""|getline o;if(o>d) print p}' log.txt