I'll affirm that what you are asking is reasonable because if the Bible chronicles things that happened in real space and time then it follows that we can apply the kind of measurable logic to confirm the truth of the matter (to a degree. Many of these things happened very long ago).

But I will also add that logic exists beyond the bounds of that which can be scientifically measured. To limit logic only to scientifically measurable proofs of physical reality is too narrow a view of logic. People believe a great many things scientific study can only poatulate about at best. I encourage you to think bigger and deeper.

Why should we believe that future experiences of things falling will be like the past? How exactly is it that we can measure anything and why should we trust that our measurements are in accord with reality? What must be true for anything to exist in reality? These are pre-scientifically measurable questions.

You might be interested in the following books:

Pushing the Antithesis by Greg Bahnsen

Why Should I believe in Christianity? By James N. Anderson

Mere Christianity by C.S. Lewis