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.
If you want to open it with administrative privileges, then use the below command instead.