This is the adverb of persuasive. If you speak, write, or argue persuasively, you do it in a way that makes people believe you or want to do what you ask. Teachers often ask students to argue persuasively in an essay: not only to have an opinion, but to give it in a way that moves the reader. It is about how you do the thing in that moment, not about whether you are a persuasive person in general. You can speak softly and still speak persuasively. It is common in school and in careful talk; a little more dressed-up than everyday chat, but not rare.

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