These questions just keep getting better and better. I happen to have just finished an argumentative essay on Julius Caesar so I'm definitely the person you want to ask. Ha.
First off, an appeal to logos is an appeal of logic. It's an argument based on solid facts.
In Scene II of Act III, we see Brutus give his speech to the Romans after having murdered Caesar. However, we also see Antony's appeal to the men of Rome in this act.
So now we have to narrow it down between the two. Was Antony's or Brutus's speech more factual? Which one used logos more?
Partiality aside, I'll have to pick Antony. I'll spare you the explanation as to why I chose him but I will post his excerpt and bolden what appears to be appeals to logos. (Remember, we're looking for facts here.)
ANTONY:
Friends, Romans, countrymen, lend me your ears;
I come to bury Caesar, not to praise him.
The evil that men do lives after them;
The good is oft interred with their bones;
So let it be with Caesar. The noble Brutus
Hath told you Caesar was ambitious:
If it were so, it was a grievous fault,
And grievously hath Caesar answer'd it.
Here, under leave of Brutus and the rest--
For Brutus is an honourable man;
So are they all, all honourable men--
Come I to speak in Caesar's funeral.
He was my friend, faithful and just to me:
But Brutus says he was ambitious;
And Brutus is an honourable man.
He hath brought many captives home to Rome
Whose ransoms did the general coffers fill:
Did this in Caesar seem ambitious?
When that the poor have cried, Caesar hath wept:
Ambition should be made of sterner stuff:
Yet Brutus says he was ambitious;
And Brutus is an honourable man.
You all did see that on the Lupercal
I thrice presented him a kingly crown,
Which he did thrice refuse: was this ambition?
Yet Brutus says he was ambitious;
And, sure, he is an honourable man.
I speak not to disprove what Brutus spoke,
But here I am to speak what I do know.
You all did love him once, not without cause:
What cause withholds you then, to mourn for him?
O judgment! thou art fled to brutish beasts,
And men have lost their reason. Bear with me;
My heart is in the coffin there with Caesar,
And I must pause till it come back to me.
If you need further explanation, please let me know in the comments section.