In facing death if he fails, Jefferson uses a targeted three part argument to sway the majority toward independence. He uses ethos, pathos, and logos to prove his case that the American colonies have no other course of action than separation.
Jefferson uses ethos to prove his credibility to the reader by showing he is a reasonable man. He does this with skill in the very introduction to the Declaration in which he shares his respect for those who must judge the colonies' decision, "a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation." The tone of his writing establishes his credibility, or ethos, which is critical to his argument.
Pathos requires eliciting feeling and emotion from the audience. Jefferson does this next, "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness." The weight of this line alone elicits emotion in the reader. Whether readers agreed with equael rights was irrelevant for his purpose of eliciting an emotional response.
The last element of Jefferson's technique is logic or logos. He appeals to the readers reason using a long list of violations of the King and Parliament on the American colony people's rights beginning with, "To prove this, let Facts be submitted to a candid world." He recounts a laundry list of crimes against the people to justify the break with Great Britain. Using irrefutable facts he proves his case and appeals to logos and leaves you with only one possible conclusion - separation from Great Britain is the only logical action for logical people to follow.