In what base does "100" equal "4 in base 10"

Question

I was reading this answer to an amusing comic related question: https://math.stackexchange.com/a/166891/35132 and I understand that in the linked answer, the examples of how four may be expressed used base (expressed in decimal!!) is 10, 4, 3 for 4, 10, 11.

What I can't figure out is what base would need to be used for his last example (100) to equal 4 in decimal?

P.S. Are maths questions like this always this hard to put in words?!

Answer 1

Let the required base be $b$. Then, $$1 \cdot b^2 + 0 \cdot b^1 + 0 \cdot b^0 = 4 \implies b = 2.$$

Answer 2

$$100_{(b)}=b^2+0\cdot b + 0=b^2 \,.$$

So 100 in base $b$ is just the number $b^2$.... Can you find $b$ now?