Question

So sánh 2³⁰ + 3³⁰ + 4³⁰ và 3.24¹⁰

Answer 1

Ta có:

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

Lại có:

\(3.24^{10}=3.3^{10}.8^{10}=3^{11}.\left(2^3\right)^{10}=3^{11}.2^{30}\)

Mà \(4^{15}>3^{11}\Rightarrow4^{30}>3^{11}\)

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

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