You don't have to use a formal writing style to write with authority. Consider this passage from my food blog, Casual Kitchen:
Both meals are roughly equal in volume and have similar satiety factors, which means you could eat either one and feel equally full for about the same length of time. Yet one breakfast has nearly three times the calories of the other. Betcha can't guess which.
This passage has an extremely casual tone, and yet it still conveys a fair amount of authority. Why?
First, it's tightly written, with few needless words. Second, it teaches the reader something, albeit in a conversational manner.
But there's a third reason this passage sounds authoritative, and it centers around the verbal contrast of the technical-sounding phrase satiety factor and all of the casual-sounding writing around it.
That verbal contrast heightens the weight of the passage. The quick use of the term, immediately followed by a clear and brief definition, suggests the author has an easy and approachable confidence in his knowledge.
This is nothing more than a rhetorical device, but it works. You welcome the reader with your friendly tone, but then show your authority by explaining, in conversational English, complicated sounding concepts and terminology.
Look for this device in articles and in the media. It's a surprisingly common technique and it's easy to imitate.
And one final note to keep my readers cynical: please keep in mind that this is just a device. Just because a piece of writing conveys authority doesn't mean the author deserves it.