“Like” and “as” are easy to get mixed up. It doesn’t help a lot to say that “as” is an adverb and “like” is a preposition. Too complicated. You might find it easier to remember, perhaps, that “as” goes with verbs, and “like” goes with nouns and pronouns.
Here’s a guy who sounds right both times, uses two different constructions, and we understand him, but he’s wrong! Take a look at the second panel in the Dec 9, 2017 edition of Mr. Fitz:
“Think like I do” sounds right. That’s because you have the verb “do,” that goes with “I.” But technically, it should be “think as I do.” By the way, it’s a good idea to include that “do” in this sort of construction; doing so removes ambiguity.
Then he hauls off and says, “think like me.” And that also sounds correct! It sounds correct because “like” feels like a preposition with that “me” all by itself after it. Well, “like” is a preposition. But he’s modifying a verb (think) with an adjective phrase. That’s a no-no. Take the book title “Black Like Me.” The color, black, an adjective, goes with the pronoun “me.” That’s correct. If he had said “a thinker like me,” since “thinker” is a noun, he would be correct, at least grammatically.
Heavy-duty grammar lesson today. Sorry.