Which number is greater $(31)^{12}$ or $(17)^{17}$ ?

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Solution

$W e k n o w t h a t 32 > 31 \to {(2)}^{5} > 31 R a i s i n g b o t h s i d e s t o p o w e r o f 12 ∴ {({(2)}^{5})}^{12} > 31^{12} \to 2^{60} > 31^{12} . . . . . (1) N o w c o n s i d e r 17 > 16 \to 17 > {(2)}^{4} R a i s i n g b o t h s i d e s t o p o w e r o f 17 ∴ 17^{17} > {({(2)}^{4})}^{17} \to 17^{17} > 2^{68} . . . . . (2) N o w 2^{68} > 2^{60} . . . . (3) F r o m p o i n t s 1, 2 a n d 3 17^{17} > 31^{12}$

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