1.) We had around 10-15 different applications, it was a messy things to track the logs as you have to login to those systems to view the logs
2.) Other issue was cleaning up of log files
Resolution for the second issue was quiet easy, one of the solution can be to write a script that will delete the logs files older then say n days and then add this script in crontab to execute with some frequency say daily. This approach had an issue, with the addition of a new system you have to do this setup every-time. As a one time solution for this problem we have created a job in our CI system(jenkins) which can be configured to run after some frequency & then reads the details of machine, location of log files which needs to be cleaned. The second approach gave us the flexibility to manage cleaning of the log files from a single place.
For first issue obviously we have to look out for some tool & the first google hit :) suggested log.io and it seemed meeting all our requirements. So the one line definition goes like this Log IO is a Real time log monitoring tool, through this tool you can monitor multiple log files in a single browser window.
I referred the link given below to configure logio
I'm not going into the details of setting up of log.io or how it works, but if you have any confusion you can leave a comment
For your reference I'm attaching an image of log.io instance we are using
So happy logs tracking :)