How do I log ALL exceptions globally for a C# MVC4 WebAPI app?

Question

Background

I am developing an API Service Layer for a client and I have been requested to catch and log all errors globally.

So, while something like an un

Answer 1

Why rethrow etc? This works and it will make the service return status 500 etc

public class LogExceptionFilter : ExceptionFilterAttribute
{
    private static readonly ILog log = LogManager.GetLogger(typeof (LogExceptionFilter));

    public override void OnException(HttpActionExecutedContext actionExecutedContext)
    {
        log.Error("Unhandeled Exception", actionExecutedContext.Exception);
        base.OnException(actionExecutedContext);
    }
}