>>Try to truncate the log. If your recovery model is simple, it means you can not restore to the point of time, you can only restore to the time your last backup was made.
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>Well, I need a full backup. I assume that if this is done every night that I should be able to take that backup and restore the database completely. Isn't this the case? Or, is it that the backup is tied to this log? Because, the most important thing is to make sure we can recover a full backup at any time, assuming we would take the one from last night. Basically, what is the standard procedure to achieve that?

Using simple recovery model you should be able to recover to last night version. All latest day transactions will be lost.

Do you have DBA? You need to test periodically your backup / restore procedures.