Logging is the process of notifying some entity of a particular event. An entity can be the system console, a file on disk, a database, or a remote computer, to name a few. Events can be simple debug information for an application in development, runtime exceptions for an application in a production environment, or a record of actions taken by a user--such as visiting a web page.
A framework is a group of classes that form the foundation for a subset of functionality in an application. Frameworks should be designed to be extendible, flexible, and adaptable to the precise requirements of any given application. And, of course, a good framework should be relatively easy to use.
Logging is important to all but the simplest of applications. You can choose to