Question

So sánh

32⁹ và 18¹³

Answer 1

\(32^9=\left(2^5\right)^9=2^{5.9}=2^{45}=2^{13}.2^{32}\)

\(18^{13}=\left(2.3^2\right)^{13}=2^{13}.\left(3^2\right)^{13}=2^{13}.3^{26}\)

\(2^{32}=2^{16.2}=\left(2^{16}\right)^2=65536^2\)

\(3^{26}=3^{13.2}=\left(3^{13}\right)^2=1594323^2\)

Vì \(65536^2< 1594323^2\)

Do đó \(2^{32}< 3^{26}\)

Nên \(2^{13}.2^{32}< 2^{13}.3^{26}\)

Vậy \(32^9< 18^{13}\)

Answer 2

Ta có:

\(32^9=\left(2^5\right)^9=2^{45}\)

\(18^{13}>16^{13}=\left(2^4\right)^{13}=2^{52}\left(^4\right)\)

Ta thấy: \(2^{45}< 2^{52}< 18^{13}\)

\(\Rightarrow32^9< 18^{13}\)

Answer 3

\(32^9\) và \(18^{13}\)

Ta có :

\(32^9=\left(2^5\right)^9=2^{45}\)

\(18^{13}>16^{13}=\left(2^4\right)^{13}=2^{52}\left(^4\right)\)

Ta thấy : \(2^{45}< 2^{52}< 18^{13}\)

\(\Rightarrow32^9< 18^{13}\)