Can anything be said to be an ultimate authority? Even god, supposedly, gives us authority over ourselves, albeit willingly, again supposedly, so even he isn't the ultimate authourity. And certainly if even god can be proven to not be the ultimate authourity, by his very nature, and the very nature of the concept of god is such that he transcends everything then logic falls well short of being the ultimate authority as logic falls well short of god and even god falls well short of ultimate authority, even if willingly, by his own admission (assuming free will). This by his own very nature, as has been presented to us at least.
So, no..even if you assume god, and certainly no if you dont. If god doesn't exist..then really humanity is little more than a function of nature, which we know is illogical since nature doesnt always favour the logical.
Also logic isn't an external process. It isn't a system of thought that is only valid if it leads to external consistency. Indeed, logic concerns itself with internal consistency. It's possible for something to be logical, and externally false. For example, it's logical for gravity to not exist, but, given context, it's false to say that it doesn't.