Re:
Hello,
I don't think a log exists for programs in Windows XP, unless programs have their own logs or explicitly integrate a log in the Windows XP Event Viewer.
But I don't think users can establish their own logs in Windows XP Home.
It does however have an Event Viewer which logs various activities, accessible in the Control Panel > Administrative Tools > Event Viewer.
There you can see which users have logged in and out of the system, with a date and time given in the Security Audit Records. All activities related to security all recorded, including successful and failed login attempts.
However, for the application log and system log, only errors are recorded, not all activity.