In literary study, "logos" usually refers to an argument or statement which is used to persuade an imagined audience. Reason is the primary method by which the narrator makes his or her case. Thus, we can say that Marvell's entire poem is an example of logos, in that an argument is developed and deployed. Life, the narrator claims, is short ("But at my back I always hear / Time's winged chariot drawing near" ); therefore, he and his Mistress should enjoy "the youthful hue" (33) while it lasts.
The poem is also laid out in a very reasonable way—the narrator begins with a fantasy of an endless life in which there is no hurry, dispels it by invoking the reality of death, then ends with the assertion that, since life is fleeting, not one moment should be wasted (that is, the Mistress should not "refuse"  his love any longer).