Question

So sánh :

\(2^{30}+3^{30}+4^{30}\) và \(3.24^{10}\)

Answer 1

Ta có : \(3.24^{10}=3^{11}.4^{15}\)

=> \(4^{30}=4^{15}.4^{15}\)

Mà \(4^{15}>3^{11}\) ( vì 4 > 3, 15 > 11 )

=>\(3.24^{10}< 4^{30}< 2^{30}+3^{30}+4^{30}\)

Chúc Bạn Học Tốt !!

Answer 2

Ta có:

\(4^{30}=2^{30}.2^{30}=\left(2^3\right)^{10}.\left(2^2\right)^{15}=8^{10}.4^{15}.\)

\(3.24^{10}=3.\left(3.8\right)^{10}=3.3^{10}.8^{10}=3^{11}.8^{10}.\)

Mà \(4^{15}>3^{11}.\)

\(\Rightarrow2^{30}+3^{30}+4^{30}>3.24^{10}.\)

Vậy.....