2010 AMC8 Problem 24

bridge

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What is the correct ordering of the three numbers, $$10^8$$, $$5^{12}$$, and $$2^{24}$$?

$$\textbf{(A)}\ 2{}^2{}^4<10^8<5{}^1{}^2$$

$$\textbf{(B)}\ 2{}^2{}^4<5{}^1{}^2<10^8$$

$$\textbf{(C)}\ 5{}^1{}^2<2{}^2{}^4<10^8$$

$$\textbf{(D)}\ 10^8<5{}^1{}^2<2{}^2{}^4$$

$$\textbf{(E)}\ 10^8<2{}^2{}^4<5{}^1{}^2$$