No, no no no. No suid for such stuff. These logs are managed by a process known as "syslog" and there is an API to send messages to this logger:
void openlog(const char *ident, int option, int facility);
void syslog(int priority, const char *format, ...);
void closelog(void);
Or you can type 'man syslog' on the command line and get all the info :-)
Update: you will need permissions to edit syslog's configuration file to send message to a separate log file, otherwise they will end up in the default location (probably /var/log/syslog).