There are numerous synonyms for the term "log zs," which generally refers to getting sleep or rest. Some of the most common synonyms include doze off, nod off, drift off, slumber, snooze, catch some z's, and get some shut-eye. All of these terms have a similar meaning and can be interchanged in most situations. Depending on the context of the situation, some other synonyms may also be appropriate, such as take a nap, go to bed, hit the hay, or lay down. It's important to choose the right synonym when expressing oneself to ensure that the message is clear and understandable.