Extended Properties are not logged into a separate column or table with the out of the box Database Trace Listener.
To log Extended Properties, configure a Formatter that logs the Extended Properties:
<formatters>
<add type="Microsoft.Practices.EnterpriseLibrary.Logging.Formatters.TextFormatter, Microsoft.Practices.EnterpriseLibrary.Logging, Version=5.0.505.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" template="Timestamp: {timestamp}{newline}
Message: {message}{newline}
Category: {category}{newline}
Priority: {priority}{newline}
EventId: {eventid}{newline}
Severity: {severity}{newline}
Title:{title}{newline}
Machine: {localMachine}{newline}
App Domain: {localAppDomain}{newline}
ProcessId: {localProcessId}{newline}
Process Name: {localProcessName}{newline}
Thread Name: {threadName}{newline}
Win32 ThreadId:{win32ThreadId}{newline}
Extended Properties: {dictionary({key} - {value}{newline})}" name="Text Formatter"/>
</formatters>
Then the Extended Property data will be logged into the FormattedMessage column.
The downside of this is that the Extended Properties are buried in the FormattedMessage. If you wanted a more structured representation of Extended Properties you could create a custom Database Trace Listener.
For an example that logs Extended Properties to a separate table see Extended Properties Trace Listener with Custom Exception Handler.