When you have logging on, the file can grow quite large, quite fast, depending on the volume of INSERT and UPDATE txns you have, size of rows, etc.
What you have to do is periodically init the log file. Good practice is to do this at the same time you do a backup. You didn't mention what OS/version of Informix you are using, etc., but with SE (what I am using right now), you have to shut down all of the connections (dbaccess, sqlexecd daemon), do the backup, and then init the log file as follows:
cat /dev/null > /yourpath/yourlogfilename
Restart the sqlexecd daemon, allow your app(s) to re-establish connections, and you are off to the races.
For purposes of controlling the server behavior when the log file fills up, I recommend keeping it in its own physical disk partition if you are in a UNIX environment.
There are any number of ways to do this, depending on your requirements (uptime, etc.), so it's hard to say what approach would be best for your particular situation.