You assume the biblical account is accurate history, a view that over a century of historical and archeological investigation does not sustain. I'll give it a try if you can first demonstrate from non-biblical sources that the story is true.
Well,
there are early, non-biblical historians who record the exodus. Certainly as historians they would have believed that what they were recording was a historical event. They didn't record these as myths, or popular legends for their time, otherwise it wouldn't be cited as extra-biblical sources.
Further, considering that we're talking about ancient times, having any type of historical record from that time is a treasure. So when you read the Exodus event in the bible, with its details about specific locations by name, people and their specific backgrounds, and profound dialogue, it presses on one that the authors of the Torah were meticulously recording their history. They, and their fathers were witnesses to all the events surrounding the exodus (i.e. parting the red sea, wandering the desert, manna from heaven, crossing the Jordan River, conquering Canaan etc).
The Book of Exodus
is the historical record of that and its surrounding events. Please remember that the exodus event was several thousand years ago, and today we're fortunate just to have remnants of the second temple (let alone the first!), and that was built 2000 to 1500 years after the exodus. New archaeological finds with biblical ties are still happening today, so there's still lots for us to discover.
And in wider scope, the entire bible is the historical record of creation, Israel, and Jesus Christ. Surely it's rich in detail concerning these things because God wanted us to have an accurate picture of these important events, people, and the background behind them. By doing this, He gave us the proper context to understand why we're here (our purpose) and where we're going (His plan for us).
what else is illogical is believing in an omniscient being.
It's illogical, and impossible, for something let alone everything to come from nothing, and the most judicial philosopher on the planet will never grant you that it can.
And when you consider the scope and magnificence of the universe from the sub-atomic to entire galaxies, it's apparent of the omnipotence that would have to behind it. An omnipotent and therefore omniscient being is not illogical if you carefully consider it.