Relevantly means “in a way that actually belongs to the subject or problem being discussed.” You use it when you add a fact or a comment and want to mark that this next bit is not a side road — it bears on the same question. It is a rather school-and-essay word. Most people just say this is relevant or this matters here, instead of putting -ly on it. You will still meet it in careful writing: someone reports a finding, and then adds, relevantly, another fact that points the same way. Though actually, it does not mean “importantly” or “very.” It is not a word for making something sound bigger. It only says the remark is on-topic.

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