Can I synchronize logs on laptop and desktop computers?

This could be done using the Observing Project Manager's import/export facility.

You can export all observations to a file and import it on another computer; no duplicates will be created on the second computer.

You can also organize your evening's work into a project and export just that project to a file.  You can import this project on the other computer.

Finally, you can select multiple items in the project pane or the observations pane and export just the selected items. Click selects a single item; Shift-click selects a range of items; Ctrl-click selects non-contiguous items.