There are several synonyms for the phrase "be led to believe" that can be used to convey similar meanings. These include "understand," "assume," "presume," "gather," "conclude," "deduce," and "infer." All of these words suggest that a person has formed a belief or idea based on information that has been presented to them, either through their own observations or through the words of others. While each of these words has slightly different connotations and nuances, all can be used to express the idea of being persuaded or convinced of something based on evidence or reasoning.