Both can be correct but the meanings are not the same. a perfect explanation << The adjective "perfect" modifies the noun "explanation." a perfect and logical explanation << "Perfect" and "logical" modify "explanation." a perfect, logical explanation << "Perfect" and "logical" modify "explanation." a perfectly logical explanation << The adverb "perfectly" modfies the adjective "logical."

It depends on what you're saying. With "I have a perfectly logical explanation", you're saying that the explanation is PERFECTLY logical, not just logical, but perfectly logical. With "I have a perfect, logical explanation", what you're saying is that the explanation is both perfect and logical. I hope it helps!

I have a perfectly logical explanation.

As said below, either could be correct, depending on what you are trying to say, however you do need the indefinite article 'a perfectly logical explanation' 'a perfect, logical explanation'