With elmah.io's appender for log4net and sink for Serilog, not only uncaught exceptions gets logged to elmah.io. Everything happening inside Umbraco gets indexed and made searchable through the UI. We support both the bundled log4net in Umbraco 7 as well as Serilog in Umbraco 8.
elmah.io is the only Error Management system that provides quick fixes, developed especially for Umbraco. Search Our directly from an error or get relevant help from the Umbraco documentation. With elmah.io you have the perfect overview of your Umbraco installation.