Can I synchronize logs on laptop and desktop computers?
Yes. You should use the backup & restore facilities to do this.
Open the Backup dialog by clicking File | Backup on the computer containing the observations that you want to copy to another computer. Make sure that at least the Observations check box is checked and click Backup to create a file containing all observations. The file must be available to the receiving computer - through a network connection or by storing it on an external storage device such as a flash drive or cloud storage.
On the computer that you want to receive observations, click File | Restore in Deep-Sky Planner on the receiving device, and select the file created in the previous step. The Observations check box should be enabled. Make sure it is checked. Click Restore. If the observations are already present on the receiving computer, no duplicates are stored.