Question

So sánh

a) 3^21 và 2^31

b) 32^9 và 16^13

Answer 1

a/ \(3^{21}=3^{20}.3=\left(3^2\right)^{10}.3=9^{10}.3\left(1\right)\)

\(2^{31}=2^{30}.2=\left(2^3\right)^{10}.2=8^{10}.2\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow3^{21}>2^{31}\)

b/ \(32^9=\left(2^5\right)^9=2^{45}\left(1\right)\)

\(16^{13}=\left(2^4\right)^{13}=2^{52}\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow32^9< 16^{13}\)

Answer 2

a)3^21=1046353203 va 2^31=2147483648

Vay :3^21 < 2^31

b)32^9=35184372088832 va 16^13=4503599627370496

Vay :32^9 <16^13