Yes. Near the upper center area of the Logs tab, there is a Show Session Log field. From the drop-down list, select either Within one day, Within three days, Within one week, Within one month, or All, to filter the list accordingly. Then click the Export button to Save the data to a file.
Note that you can also use the Search field to filter the data. Enter the character(s) you want to search for, then click the Search button. Each log entry in Splashtop Center will be searched for matches to the string you entered in the Search field. Click Reset to return the list of log items to its status prior to searching.