linux – What is the best way to maintain application logs

We have an SaaS application (LAMP stack) hosted in-house, used by thousands of clients on daily basis. Application generates logs (whether an error occurs or certain events happens inside the application/frontend servers) and sends them to a specific email address. We receive over 400-500 such notification emails per day which is not a good approach. The reason of having this approach is that we want to get notified instantly and take an action accordingly.

I am sure there are more standardized ways of managing logs and have some sort of dashboard which we can review regularly (multiple times a day) and see if there is any urgent issue.

Some of the notification types we receive are:

  1. PHP specific errors
  2. Server-to-server communication errors
  3. Application specific issues (based on user input, API integrations etc)
  4. Server maintenance / Hardware issues