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.

pre-writing

why we feel good, or better, when we laugh?

is there a scientific explanation for this to happen?

which are the sources?

rough draft

laughter has a way of instantly connecting people and is one of the most basic and fundamental ways in which we communicate as human beings.

newport academy: endorphins reduce stress and strength social connections.

they combat anxiety and depression.

final draft

we know that when we laugh we feel better; when something is making us laugh it means we thought it was funny at some point, even if it was not meant that way. what we know is that it made us feel good. that is something we all can realize easily, but is it a chemical explanation for it to happen? of course there

according to joe bluett, laughter has a way of instantly connecting people and is one of the most basic and fundamental ways in which we communicate as human beings. also, he says that laughter can increase confidence, self-esteem, creativity, positivity and resilience, bringing positive changes to all aspects of our lives.

the newport academy says that, when we laugh, we release endorphins and that makes our body feel instantly relieved from tension and worry. endorphins also reduce stress and strength social connections.

therefor, laughter is the best to combat anxiety and depression.