In Act 1, Scene 1, Sampson, a servingman of the house of Capulet, employs logos as he jokes around with another Capulet servingman, Gregory, in the town square:
Sampson: A dog of that house shall move me to stand. I will take the wall of any man or maid of Montague’s.
Gregory: That shows thee a weak slave, for the weakest goes to the wall.
Sampson: ’Tis true, and therefore women, being the weaker vessels, are ever thrust to the wall. Therefore I will push Montague’s men from the wall and thrust his maids to the wall.
Sampson boasts that by walking on the side of the street nearest to a wall, he will force "any man or maid of Montague's" into the street, demonstrating his own brute strength. Gregory chides him for his arrogance by setting out a premise: "the weakest," he claims, "[go] to the wall." In response, Sampson uses logos to reverse his original claim while still boasting about his own strength. Employing Gregory's premise, he will "thrust" Montague women to the wall, since women are "the weaker vessels." This logical conclusion also contains a threat of sexual violence: Sampson is boasting that he can have his way with Montague women without their consent.
Sampson's use of logos is a tactic to persuade Gregory—and the audience—that he has courage, fortitude, and sexual prowess, framing his exaggerated claims about himself as logical, reasonable ones. He is far from the only character in the play to use sexual innuendo or joke about sexually assaulting women. The Montague servingmen (Mercutio in particular) do as well, clearly indicating that Verona is a patriarchy: women are rendered defenseless and judged as objects that men can control.
Moreover, Sampson's crude (if logically reasoned) joke is just one example of numerous moments in the play in which language is used as a weapon: to exert force, demonstrate power, and diminish those the speaker views as inferior—in this case, both women and Montagues in general.
In Act 4, Scene 1, Juliet—having learned that her family is about to marry her to Paris—goes to Friar Laurence and threatens to kill herself. Friar Laurence begs her not to and hastily devises a solution, which he persuades her to agree to through the use of logos:
Hold, daughter, I do spy a kind of hope,
Which craves as desperate an execution
As that is desperate which we would prevent.
If, rather than to marry County Paris,
Thou hast the strength of will to slay thyself,
Then is it likely thou wilt undertake
A thing like death to chide away this shame,
That cop’st with death himself to ’scape from it;
And if thou darest, I’ll give thee remedy.
Friar Laurence recognizes that Juliet is desperate to avoid marrying Paris; his kindness and commitment to pacifism make him sympathetic to the young lovers' plight. Moreover, since Friar Laurence has married Romeo and Juliet in secret, he knows that Juliet's marriage to Paris would not be valid—adding further complications to an already dire situation.
Friar Laurence seems to understand that ordering Juliet not to kill herself would be fruitless. She is overcome with fear and grief, and has already rebelled against instructions from the other adults in her life (namely, her parents and her Nurse, who have all encouraged her to marry Paris). Thus, he employs logos to try to reason with her, making use of her unstable mental state. If Juliet has the "strength of will" to kill herself, he reasons, then she will also have the strength to take a sleeping potion and experience a kind of temporary death by falling into a deep sleep. Then, upon waking, Friar Laurence will lead her to Romeo in Mantua. Additionally, by framing the plan as something Juliet will agree to only if she "darest," Friar Laurence is subtly taking advantage of Juliet's desperation—challenging her to prove both her love for Romeo and her own courage to rebel.
Friar Laurence's use of logical reasoning stands in opposition to Juliet's hysteria and panic. He seems to be in control of the situation, and Juliet puts her trust in him to follow along with the plan. Ironically, however, Friar Laurence's plot goes awry (when an expected message to Romeo informing him about Juliet's "death" does not arrive in time), emphasizing a major theme of the play: adults are no less fallible than children, despite their apparent wisdom. Ultimately, Friar Laurence's logical reasoning is rendered futile. In taking the potion, Juliet briefly experiences "a thing like death," just like Friar Laurence promised—but then she actually dies by suicide.