Every plugin has its own logger already available. Its usage is described in a short FAQ page on the Eclipse website. The main benefit of using that logger is that your plugin shows its logging entries in the error log view of Eclipse like every other plugin. If you want to deploy your plugins as Eclipse application, you can then have the error log view bundled in a separate optional feature, so that your users can choose to have this log view in the application available or not.
There is also another FAQ about all the available log files. But if you use the error log view, you will normally not need to search or manipulate the log file directly. And also for end users, it is probably more convinient to look at the errors directly in the application, with the possibility to export the log directly from the UI.