It is fundamentally impossible to "show" someone else the truth of a leap of faith. All that one can do is invite someone to make their own leap, based on their own experience, intuition and judgement. Faith is always personal, even if it relates to conclusions which are commonly held. The belief which I hope you have in "the validity of logic" is your own personal belief, even though it relates to "logic" which is something owned by all rational people.
Faith can provide us with certainty of a kind; but faith is only "practical certainty" - the certainty needed for action: Newman called this "certitude" - not the "theoretical certainty" of mathematics. We choose to believe certain things because this belief offers us a way forward which has the appearance of being fruitful and wholesome and life-affirming.
This is why we "believe in logic", at first; because we can see that if logic were to be reliable it would enable us to achieve a great deal, whereas if logic is unreliable very little is achievable. Subsequently, we find that we are able to achieve a great deal on the basis of logic and this corroborates our faith in its wholesomeness: but no amount of positive experience can ever turn our original act of faith into a mathematical proof.
Faith should tell us how reality actually is, if the belief (doxa) is a true belief (ortho-doxa). This is what we hope is the case, but can never be sure is so. This is the dilemma of faith. Faith deals with the most basic and important things and enables us to grow and learn on the basis of us having accepted these foundational principles with certitude and by faith; and yet we can never have true-and-certain-knowledge (episteme) of what the principles which faith proposes and upholds... unless and except by some intuitive leap of apprehension from the uncertain foundation of empiricism to the solidity of some spiritual reality which underlies material existence.