Question

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

Answer 1

Ta có:

\(3.24^{10}=3.\left(2^3.3\right)^{10}=3.2^{30}.3^{10}=3^{11}.2^{30}\)

\(4^{30}=\left(2^2\right)^{30}=2^{60}=2^{30}.2^{30}=4^{15}.2^{30}\)

Dễ thấy \(3^{11}.2^{30}< 4^{15}.2^{30}\)

\(\Rightarrow3.24^{10}< 4^{30}< 2^{30}+3^{30}+4^{30}\)

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