Normally, it would go to one of your core projects (having no dependency on other projects). So that it can be used from all of the solution.
The configuration required for Log4net is saved in the web.config, but the logger class can be in any other project.
[update - to answer questions in the comment - well which are mostly answered by @Justin]
Generally, Logging is implemented as an abstract class/interface where all required methods are declared like log, error, warn etc.
Then you write implementation of this interface using a library of your choice, e.g. Log4Net
You need to add reference to log4net (or any other library that you choose) in your this project.
You need to keep it flexible so that you can change the library without changing the code everywhere else in the solution.
e.g. For your production logging you use ApplicationInsight but for local dev you use log4net implementation.
A factory might be needed to get the correct type of logger depending on your environment/configuration.
All configuration related to Log4Net are kept in the web.config because it is the startup project. Also, it allows configurable properties for the library e.g minimum log level.