Which number is greater $(30)^{100}$ or $2^{567}$ ?

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Solution

$W e k n o w t h a t 32 > 30 \to {(2)}^{5} > 30 R a i s i n g b o t h s i d e s t o p o w e r o f 100 ∴ {({(2)}^{5})}^{100} > 30^{100} \to 2^{500} > 30^{100} . . . . . (1) N o w c o n s i d e r 2^{257} N o w 2^{257} > 2^{500} . . . . (2) F r o m p o i n t s 1 a n d 2 2^{257} > 30^{100} ∴ 2^{257} i s g r e a t e r$

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Which number is greater (30)100 or 2567?

Weknowthat32>30→(2)5>30Raisingbothsidestopowerof100∴((2)5)100>30100→2500>30100.....(1)Nowconsider2257Now2257>2500....(2)Frompoints1and22257>30100∴2257isgreater

Which number is greater $(30)^{100}$ or $2^{567}$ ?