If you inherit all your classes from Logging class then you won't be able to inherit classes from any other classes and create inheritance structure because C# does not support multiple inheritance. You really need to use composition not inheritance.
You can simplify calls to your logger by creating static helper class:
public static class LoggerHelper
{
public static void WriteError(string message,Exception ex, Type type)
{
var log = log4net.LogManager.GetLogger(type);
log.Error(message, ex);
}
}
And then in you classes you will call it like this:
public class MyClass
{
try
{
// do something
}
catch(Exception ex)
{
LoggerHelper.WriteError("Problem doing something", ex, this.GetType());
}
}