Hey guys, back the longest question string I have ever posted again: What is the shape of the graph, and why is the self-intersection point (e,e)?

Original Link: http://web2.0calc.com/questions/very-hard-math-question-for-my-profile-picture

I messed this up and started something really bad before, so I'll just say what I know:

Part A: \(x^y=y^x\)

Part B: \(x\log_y=y\log_x\)

Part C: (e,e)

Part E: One of them is y=x, please help me with the 2nd!

helperid1839321
Nov 2, 2017