On some phones logcat allows to get the log information from previous reboot with the -L option, it would be great to get it, see MVT. (the right command to get everything with logcat is logcat -d -b all \"*:V\").
You can store the old logcat info in a logcat_old.txt file.
(Note that some phones don't support that option, so the command may return an error you can ignore)