Welcome to the AndroidForums, rfburns59!
I've moved your thread over to the all-things-root area for you.
Any apps you've got installed will probably maintain their own logs in their own home filesystem space (
/data/data/<package name>).
Android is a different animal as far as the /var/log directory goes: there's no syslogd daemon.
There are also
kernel messages you can view (all yield the same output):
- on phone, at shell prompt:
dmesg
- on phone, at shell prompt:
cat /proc/dmesg
- via adb from your PC:
adb shell dmesg
- via adb from your PC:
adb shell cat /proc/kmsg
Also, don't forget about the
logcat feature that will enable you to view the various log file messages that apps and processes record:
- on phone, at shell prompt:
logcat
- via adb from your PC:
adb logcat
See this link for more information:
How to get kernel messages from Android? - BootLoader
Cheers and I hope that helps!