There is a module to also retrieve the Mendix logs in your application. But depending on what you want to do it might be better to create your own logging. In our application we always have a log and a logdetails object. And anytime we want to log something we use these objects. Then you can also easily create graphs or expose those logs to other systems. And why two objects? Because if you iterate over a list for instance we create one log for the microflow(s) and use logdetails for the specific points or iterations we want to log.
Regards,
Ronald
You can use the Core.registerLogSubscriber API to setup a custom logging implementation. That's what other existing Logging modules use (Logging or SapLogging module).
It's wiser to use and external service like splunk which already has the option for reporting.