How to merge log files and sort by time
Ref: Merging multiple log files by date including multilines
As mentioned in the above question, if you are certain that all the log lines start with timestamp, you can do:
cat logA.log logB.log | sort -n
This would not work when there are other lines such as stack trace which do not start with timestamp.
I think you can check out the above question and answers if your considering a similar scenario.