There are a number of approaches you can take here. If you want to have an experience that is like writing directly to the filesystem, then you could look at using something like s3fs to mount a common S3 bucket to each of your instances. This would give you more or less a real-time log merge though honestly I would be concerned over the performance of such a set up in a high volume application.
You could process the logs at some regular interval to push the data to some common store. This would not be real time, but would likely be a pretty simple solution. The problem here is that it may be difficult to interleave your log entries from different servers if you need to have them arranged in time order.
Personally, I set up a Graylog server for each instance cluster I have, to which I log all my access logs, error logs, etc. It is UDP based, so it is fire and forget from the application servers' standpoint. It provides nice search/querying tools as well. Personally I like this approach as it removes log management from the application servers altogether.