Take the medicine as prescribed. As there is no verb to be in this sentence, is it passive because it is implied? ..i.e., Take the medicine as (it was) prescribed.?
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The main clause is take the medicine..., which is active, because its main verb is active, take. Because the main clause is active, the sentence is active.
The past participle prescribed is passive. You can read it as an elliptical clause, as it was prescribed, or as a mere participial construction; in either case, it's passive, but the sentence as a whole is still active as above. The verb to be is not what would make it passive: the passivity is located in the past participle. It just so happens that past participles are often combined with to be.