Log to elmah.io from the default Sitecore log4net implementation.
First, make sure that you have installed the elmah.io NuGet package into your solution, and that you have added all of the necessary configuration to the Sitecore Web.config file.
For more information on how to install elmah.io, please refer to the section Configure elmah.io manually found on elmah.io documentation.
Once installed, you need to configure your elmah.io log ID in the configuration file, found under App_Config/Include/Elmah.io.Sitecore.log4net.config.