Question

21¹⁵ và 27⁵.49⁸

8¹⁵ và 3³⁰  So sánh 2 số

Càng nhanh càng tốt nha

Answer 1

a)     \(21^{15}\)\(=\left(3.7\right)^{15}\) \(=3^{15}.7^{15}\)

\(27^5.49^8\) \(=\left(3^3\right)^5.\left(7^2\right)^8\)\(=3^{15}.7^{16}\)

Ta thấy    \(7^{15}< 7^{16}\)\(\Rightarrow\)\(21^{15}< 27^5.49^8\)

b)     \(3^{30}\)\(=3^{2.15}\)\(=\left(3^2\right)^{15}\)\(=9^{15}\)

Ta thấy     \(8^{15}< 9^{15}\)

\(\Rightarrow\)\(8^{15}< 3^{30}\)

Answer 2

Ta có: \(21^{15}=\left(3.7\right)^{15}=3^{15}.7^{15}\)

\(27^5.49^8=3^{3.5}.7^{2.8}=3^{15}.7^{16}\)

Vì \(15< 16\)nên \(7^{15}< 7^{16}\Rightarrow3^{15}.7^{15}< 3^{15}.7^{16}\)

Hay \(21^{15}< 27^5.49^8\)

Ta có: \(3^{30}=3^{2.15}=9^{15}\)

Vì \(8< 9\)nên \(8^{15}< 9^{15}\)

Hay \(8^{15}< 3^{30}\)