In C we log this way:
syslog( LOG_INFO, \"proxying %s\", url );
In Linux how can we check the log?
tail -f /var/log/syslog | grep process_name
where process_name is the name of the process we are interested in
How about less /var/log/syslog?
By default it's logged into system log at /var/log/syslog, so it can be read by:
tail -f /var/log/syslog
If the file doesn't exist, check /etc/syslog.conf to see configuration file for syslogd.
Note that the configuration file could be different, so check the running process if it's using different file:
# ps wuax | grep syslog
root      /sbin/syslogd -f /etc/syslog-knoppix.conf
Note: In some distributions (such as Knoppix) all logged messages could be sent into different terminal (e.g. /dev/tty12), so to access e.g. tty12 try  pressing Control+Alt+F12.
You can also use lsof tool to find out which log file the syslogd process is using, e.g.
sudo lsof -p $(pgrep syslog) | grep log$ 
To send the test message to syslogd in shell, you may try:
echo test | logger
For troubleshooting use a trace tool (strace on Linux, dtruss on Unix), e.g.:
sudo strace -fp $(cat /var/run/syslogd.pid)
                                                                        If you like Vim, it has built-in syntax highlighting for the syslog file, e.g. it will highlight error messages in red.
vi +'syntax on' /var/log/syslog
                                                                        A very cool util is journalctl. 
For example, to show syslog to console: journalctl -t <syslog-ident>, where <syslog-ident> is identity you gave to function openlog to initialize syslog.
On Fedora 19, it looks like the answer is /var/log/messages. Although check /etc/rsyslog.conf if it has been changed.