atutor2001:So which of your first two extracts says that louder is wrong in formal speech?Extracted from http://oald8.oxfordlearnersdictionaries.com/dictionary/loud_2Zack7:
No. Louder in here is a comparative adverb. It modifies the verb speak. So is more loudly. And both are acceptable in formal writing.
\"Louder is also used in informal styles to mean ‘more loudly’: Can you speak louder?\"
Extracted from http://www.funtrivia.com/askft/Question97662.html
In speech, 'quicker' would be the most commonly found. In formal document writing, 'more quickly' would be found
In this link http://forum.wordreference.com/showthread.php?t=1335298 they even disallowed \"louder\".
And also, I can quote you a ton of other sources that says otherwise.
And the last link first comment by lis, louder is an adverb, not an adjective. she is wrong.
English is not a one way street. It is not rigid. Different sentence structure can mean totally different things and a fine line normally separates the right from the wrong if there is even a right and a wrong in the first place.
What might be wrong now may be accepted in future. Language evolves.
And louder seems wrong there because of the sentence structure. It is different from the question here.
Can you speak louder vs can you read all the new words more loudly.
In fact the better choice Is can you read all the new words aloud.
Because there is no hint of comparison there as opposed to the question here. So it is not as good to use comparative adverbs there.