Knowing math jokes helps for the Putnam!

I spent 6 hours on Saturday 12/1 on the Putnam 2012 Exam. In both parts, I solved the first two problems in an hour, and spend the remaining two hours making no progress. But my favorite part of the exam was how I solved B1.

Let $S$ be a class of functions from $[0,\infty)$ to $[0,\infty)$ that satisfies:

(i) The functions $f_1(x)=e^x-1$ and $f_2(x)=\ln(x+1)$ are in $S;$

(ii) If $f(x)$ and $g(x)$ are in $S,$ the functions $f(x)+g(x)$ and $f(g(x))$ are in $S;$

(iii) If $f(x)$ and $g(x)$ are in $S$ and $f(x)\ge g(x)$ for all $x\ge 0,$ then the function $f(x)-g(x)$ is in $S.$

Prove that if $f(x)$ and $g(x)$ are in $S,$ then the function $f(x)g(x)$ is also in $S.$

This probably at first looked super complicated, and I wasn't sure how to start. But then I thought of the following math joke:

Noah's Ark lands after The Flood and Noah releases all the animals, saying, "Go forth and multiply." Several months pass and Noah decides to check up on the animals. All are doing fine except a pair of snakes. "What's the problem?" asks Noah. "Cut down some trees and let us live there," say the snakes. Noah follows their advice. Several more weeks pass and Noah checks up on the snakes again. He sees lots of little snakes; everybody is happy. Noah says, "So tell me how the trees helped." "Certainly," reply the snakes. "We're adders, and we need logs to multiply."

(Source: http://www.math.utah.edu/~cherk/mathjokes.html)

And soon after I remembered this joke, I wrote down a solution!