Question

so sánh

a. \(2^{225}\) và \(3^{150}\)

b. \(2^{91}\) và \(5^{35}\)

c. \(99^{20}\) và \(9999^{10}\)

Answer 1

a) Ta có: \(2^{225}=2^{3.75}=\left(2^3\right)^{75}=8^{75}\)

                \(3^{150}=3^{2.75}=\left(3^2\right)^{75}=9^{75}\)

\(\Rightarrow8^{75}< 9^{75}\)\(\Rightarrow2^{225}< 3^{150}\)

b) Ta có : \(2^{91}=2^{7.13}=\left(2^{13}\right)^7=8192^7\)

                \(5^{35}=5^{5.7}=\left(5^5\right)^7=3125^7\)

\(\Rightarrow8192^7>3125^7\)\(\Rightarrow2^{91}>3^{35}\)

c) Ta có: \(99^{20}=99^{2.10}=\left(99^2\right)^{10}=\left(99.99\right)^{10}\)

               \(9999^{10}=\left(99.101\right)^{10}\)

Vì 99<101 \(\Rightarrow\left(99.99\right)^{10}< \left(99.101\right)^{10}\)\(\Rightarrow99^{20}< 9999^{10}\)