Is this sentence correctly written? logos, the appeal to logic; persuasion that  is backed  up with actual  observations, data, and facts.

The message is understood but the sentence is not well written. You should write "Logos, that is the appeal of logic, consists of persuation backed up with actual observation, data, and facts". While the word Logos can be paraphrased as 'the appeal of logic', it is necessary to clarify the function of Logos in a text. With that purpose in mind, it is neccesary to separate the ideas of persuation from the paraphrase.

first of all wood chucks don't "chuck" wood. none, and for the fun of the answer the amount of wood chucked would be a lot!

explanation:

a wood chuck is a ground hog, it belongs to the family of large underground squirrels. it belongs to the family of marmots. ground hogs eat grasses, berry's, and other vegetation.