The ‘system log’ in Ubuntu (or in any other OS) is not something that most users are interested in or use that much. However, it is a pretty useful tool that lets you track back software or hardware related issues etc.
And for some reason, in Ubuntu 12.10, I cannot open it by clicking on its icon in Unity’s ‘Dash’. I don’t know if it is a system wide bug, but if you are too having the issue, then until a fix comes in, you can still open it by using the below command in your Terminal window.
gnome-system-logIf you want to open it with administrative privileges, then use the below command instead.