Certainly X would denote 'times' or 'multiply by.' However, there should be a space between the number and X. (2 X, 10 X). May also be written as X 2, X 10. Writing 2X would suggest an algebraic notation.

Typically I would use 2x (lowercase x) if I were saying "My dog has grown 2x in size." In formal writing, you should spell it out (My dog has grown two times in size.). If it is used in a math problem (two times two) I would use 2*2 or 2x2. Hope that answers your question!