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Which of the following is true?
Question

Which of the following is true?

A.

πππ<eee<333\pi^{\pi^{\pi}} < e^{e^e} < 3^{3^3} \\​​

B.

πππ<333<eee\pi^{\pi^{\pi}} < 3^{3^3} < e^{e^e} \\​​

C.

333<eee<πππ3^{3^3} < e^{e^e} < \pi^{\pi^{\pi}} \\​​

D.

eee<333<πππe^{e^e} < 3^{3^3} < \pi^{\pi^{\pi}}​​

Correct option is D

Given:We need to compare ππ, ee, and 33.Solution:ee=2.71832.718315.1533=27ππ=3.14163.141636.46Thus, we have ee<33<ππ.Correct Answer: (D) ee<33<ππ\textbf{Given:} \\\text{We need to compare } \pi^{\pi},\ e^{e},\ \text{and } 3^{3}. \\[6pt]\textbf{Solution:} \\[4pt]e^{e} = 2.7183^{2.7183} \approx 15.15 \\[4pt]3^{3} = 27 \\[4pt]\pi^{\pi} = 3.1416^{3.1416} \approx 36.46 \\[6pt]\text{Thus, we have } e^{e} < 3^{3} < \pi^{\pi}. \\[10pt]\boxed{\text{Correct Answer: (D) } e^{e} < 3^{3} < \pi^{\pi}}​​

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