DriveHQ does have detailed download log and web access log. However, as we have so many users and heavy activity everyday, it is not possible to make the information available for online query.
We do provide some activity logging to meet your needs partly. You can log on www.drivehq.com, click on Publish. In the Manage Publish page, you can see a column named: "Times visited". This stands for the number of users who have accessed your published folder. It doesn't tell if the user has downloaded your file. You can then check your account balance. Look at the download bytes field. When a user downloads your file, it is using your download bytes. So after you refresh your account balance, you can easily calculate the number of downloads.