You do not indicate your OS version, but I'll assume 10.3.9 (probably is similar for different systems anyway). Do a "file find" for the following two files:
console.log
system.log
I think you will find that each user has its own console.log in its own folder. However, system.log is in a general log folder and should have read access by the administrator group, and presumably you are an administrator -- if not you will not be able to view the system log, that is by design of the OS.
If you are not an administrator, you will need to log in as one to view the system log. Or, if you are an administrator, you can change the permissions on that file so that you can have read access.