Which of the following best captures the meaning of "cogent"?

The term "cogent" refers to arguments or reasoning that are clear, logical, and convincing. It is often used to describe statements or points made that effectively persuade someone due to their clarity and forcefulness. Therefore, the choice that suggests "powerfully persuasive" aligns perfectly with the meaning of "cogent," as it emphasizes the strength and effectiveness of the argument in compelling someone to understand or accept a particular viewpoint.

In contrast, the other options highlight characteristics that are contrary to the essence of being cogent. For example, terms like "weak and unconvincing," "vague and unclear," and "inconsistent and variable" suggest a lack of clarity, strength, or persuasiveness, which directly contradicts the definition of cogent arguments. Therefore, "powerfully persuasive" stands out as the appropriate description.