If your question means, is it possible to express any sentence of a natural language such as English in a logical formalism, such as first order predicate logic (FOPL), then the answer is no. Natural languages are richer and more expressive than formal ones.
Consider FOPL, such as you might learn it from an introductory text book. It does not have the resources to express indexicals such as "I", "you", "here", "now", etc. So you cannot express "I am hungry". The nearest you can get is Hungry(john) where john is your name. It only allows quantification over things, not properties, propositions or classes, so you cannot express, "everything John says is true". It does not as standard quantify over entities such as events, so you cannot say "John ran quickly so John ran" - although Davidson made a good showing of how we might remedy that limitation. It does not allow you to quantify over fictional or hypothetical entities. It does not have the resources to express temporal relations such as "it was raining yesterday but not today" - although again there are temporal extensions to logic that can help. It does not express modal relations such as "it is possible that...", "it is obligatory that...", "you must...". Again, modal logics attempt to fill in this gap with partial success. It does not express speech acts such as questions, promises, threats, expostulations, etc., e.g. it cannot express the simple sentence "Damn!", let alone something subtle like "I now pronounce you husband and wife". It does not express the attributive nature of some adjectives, e.g. "this is a good knife" does not simply mean this is good and this is a knife. It does not attempt to express pragmatic features of language use, such as conversational implicatures, e.g. it does not express the fact that "A and B" might carry the implicature of ordered events. It cannot cope with intensional contexts such as the propositional attitudes, e.g. "Mary thinks that...", "John hopes that...", "Carol fears that...". It is bivalent, so it does not cope well with statements where one might say there is a degree or truth, or no truth of the matter, such as vague statements.
Some of the above limitations can be overcome by using extensions to logic, e.g. temporal logic, modal logics, higher order logics, etc., but (a) none of these work completely, (b) the more complex you make the logical apparatus, the less likely you are to have a proof system or model system for it, so there is a diminishing return in utility, (c) there is still a substantial residue of English usage that does not fit.
FOPL and its extensions are still very useful. I hope I haven't put you off studying it. But it is well to understand their limitations.