Tools - Log Viewer. I think the default display may be just 30 days. Use the drop down list to change it to Custom and enter a date parameter. Also, the filter may be set to just show Warnings, for example. Change the filter to No Filter. Click on Export. After you export the file to excel or xml file, Tools - Log Viewer - Archive - Archive and Delete. In both steps you may choose the location of where to save the files.

Running as Security Administrator. There is still no option to "Archive and Delete."

Running as Security Administrator. There is still no option to "Archive and Delete."

Correction. Archive and Delete is now available. I had to log out/in.
So, the ability to Delete log entries is dependent on Security roles.