Yes, you could have used calculator trickery. You could have made nasty assumptions and pulled out dirty answers. In the end, you would even have gotten the same answer as me and wasted a lot less of your life thinking about it. But the fact of the matter is undeniable. The problem is beautiful. It's the first problem I've ever seen bring natural logarithms to their knees. I've never hit an indeterminate form outside of calculus. And yet here it is.
If the problem is beautiful, the solution is even more so.
Enjoy.
(click the thumbnail to view the full solution)
