text: This problem was part of a Montgomery County Math competition a few years ago, and I’ve had it posted on my whiteboard for the past two weeks:
  If you haven’t at least tried it, go ahead and do it now. Then check out the solutions below. Sorry it’s so long!
  Here’s one solution (stay with me on this!). Rewrite in log form and do some algebra, applying some log properties:
  Did you see that? That was amazing! We wrote the discrimant as a perfect square. Pretty cool. Let’s not get too excited though. Finishing the problem:
  Arun’s Solution. Now, I’d like to share how one of my students, Arun, solved the problem in a slightly more elegant (or quicker, at least) way. First, we introduce a new variable,