Looking on the internet deeply has found these results:

illogical is the most popular phrase on the web.

unlogical 1117,000 results on the web	illogical 19,500,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	It would be illogical for Apollo to kill us. That would be highly illogical as I am already outfitted... Hear... the strange and illogical but genial rhythm... A fear of heights is illogical. I find it illogical that its intentions be hostile. I submit to you that your empire is illogical. It goes to their... illogical passion for winning at all costs. This is absolutely illogical and clearly at odds with Community law respecting abuse of a dominant position.

unlogical

1117,000 results on the web

illogical

19,500,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

It would be illogical for Apollo to kill us.
That would be highly illogical as I am already outfitted...
Hear... the strange and illogical but genial rhythm...
A fear of heights is illogical.
I find it illogical that its intentions be hostile.
I submit to you that your empire is illogical.
It goes to their... illogical passion for winning at all costs.
This is absolutely illogical and clearly at odds with Community law respecting abuse of a dominant position.