How to restore a database from the SQL 2008R2 log?
There is no free tool to do this. Basically, your only other option is to restore a backup. For that you need to have made a full backup of the database. If you have one, you can recover your table at the time of your full backup by restoring it into another database, and copy the table back to your original database.

Plus, if your database is in full recovery model, you can backup your transaction log and try to restore it after the full backup restore and other transaction log backups that you might have taken in between if you have a backup plan.
So, do you have backups of your database, and when were they taken?