You can delete individual log entries by selecting them in the DropDMG window and pressing delete. Use Edit ‣ Select All to quickly clear the log.
The pop-up menu lets you set DropDMG to automatically delete old log entries When DropDMG quits, After one day, After one week, After two weeks, After one month, or After one year. If you set it to Manually, DropDMG will keep the log entries forever (unless you delete them).