Windows 7: How to automatically trigger the execution of a script on logout

I wish I could start running a little script that writes the date and time a file on each machine at off time, but at every logout a user of machine (home premium in Windows 7). How can I do this? And ya in this for the performance at each connection, I understood it enough to put the script in the Startup folder, but there is no record of extinction or something like that?

I think this question is about the script, not the script itself having no home, can you check if you have a task scheduler available
- Start Menu-> Accessories-> System Tools-> Task Scheduler
- Click on "Library of planning sequence"
- In the middle window, do it right then -> Create New Task
- Trigger tab -> click New
- In the "Start Task" -> you select "When disconnecting a user session"
- Remember to check that box "Enabled" is acitve
- Back in the interface, think of a name to save your work in "General"
- And the order of your script must be entered in the "Actions"

Thank you for the reply, but

1. My question is on logoff (for logon, is it not easier to put the script in the start folder for each user? In the DC area where it must save the script in the article that you point does not exist!)
2. I stress that my request is for a home premium version is no possible way gpedit.msc as I do not have any other option. My question still remains unresolved!

I am also a facing the same issue which is of "trigger end of the session," because I have to test it, it actually works when I switch users but not at shutdown or just find session.
So the problem remains.
Where it works:
- Switch User
If it does not work
- Closing Session
- Stop / Restart the computer
Should I assume that the actual closing of the session is the problem? Thank you in advance