The command that will accomplish the task of finding and removing all log files that were modified more than 180 days ago is find /var/log -type f -mtime +180 -exec rm {} ;. This command will use find to search for files (-type f) under /var/log directory that have a modification time (-mtime) older than 180 days (+180). For each matching file, it will execute (-exec) the rm command to delete it, passing the file name as an argument ({}). The command will end with a semicolon (;), which is escaped with a backslash to prevent shell interpretation.