Is it appropriate to use the word “like” in a research paper? In a research paper, is it appropriate to use the word like meaning similar or similar to? For example the sentence:


  Like in Eq.(2), we will substitute y in Eq.(6) to simplify the equation.
The word "like" is perfectly OK, but your use of it in the example sentence is wrong. It should be "as" [[because the clause "Like in Eq. (2)" modifies the verb phrase "will substitute" and thus functions as an adverb.  "Like" produces adjective phrases and would be correct if you were modifying a noun.]]  For example, it would be correct to write "This simplification is like the one in Eq. (2)."

EDIT: What I wrote about the example sentences is right, but the reason I gave, now in brackets [[...]] above, is wrong. In particular, a "like" phrase can function as an adverb; "he sings like Caruso" is correct.  The difference between "like" and "as" (when they express similarity --- both words have several other meanings) is that "like" is a preposition and "as" is a conjunction. So "like" should form a phrase with a noun, e.g., "like the one in Eq. (2)", and "like Caruso".  "As" should be followed by a whole clause, like a sentence, but much of that clause is often omitted. Thus, for example, "As in equation (2), we will substitute ..." is an elliptical form of "As we did in equation (2), we will substitute ...".