Max Caulfield doesn't interact much with Logan. He is generally rude and dismissive towards her. He seems absent-minded most of the time, and is a bully on campus. In his letter to Dana he admits that he would only act like a "tough jock" around everybody else, but that he was able to show his true self around her. He didn't take responsibility for his child because he was scared of this responsibility which probably led to their break-up, admitting it himself in his letter, only offering financial support to Dana later.
When Max is going to the bathroom, she sees Logan bullying Daniel DaCosta and wishes she could beat Logan up in revenge. Max rewinds time and as she goes to the bathroom again to save Chloe Price from being shot by Nathan Prescott, she doesn't consider that Logan could help her. Later, Max can spot Logan playing football with Zachary Riggins outside the Prescott Dormitory. He will tell Max to wait until Friday's sports game to take photos of him, and continues to play with Zach.
In Dana's room, we can find a crumpled up letter from Logan regarding their previous relationship and his desire to reconnect and help her with her pregnancy. We can assume that he is the father of her aborted child, as Dana Ward confirms that the father is a football player; but not Zach. The text of the letter is as follows:
Dana I suck at writing but I thought I should write this so you might not hate my dumb ass forever. I know I act like a tough jock around everybody but I never had to act around you, I'm not the kind of man you deserve. You saw how I pussed out.
if you need any money, let me know. XO Logan
Logan makes an appearance at the Vortex Club's End of the World party, in the VIP section. He tries to flirt with Max. Max can confront him about his attitude towards others and his treatment of Dana. If she asks him about Dana, he will say he feels bad for "flaking on her". If spoken to about Nathan, he will tell Max he hasn't seen him tonight, comment about the Prescotts' wealth and advises Max to speak to Victoria because "she always knows where Nathan is".