Question

[Nguyễn Anh Chiến 2k8]

So sánh 2 mũ 9 / 3  mũ 2010 VÀ 3 mũ 9 / 2 mũ 2010

Answer 1

[Xyz OLM]

Ta có : \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1^{2019}=1\)

Vì \(\frac{2^9}{3^{2010}}:\frac{3^9}{2^{2010}}< 1\)

=> \(\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

Answer 2

[Bellion]

       Bài làm :

Cách 1:

Ta có :

 \(\frac{2^9}{3^{2010}}\div\frac{3^9}{2^{2010}}=\frac{2^9.2^{2010}}{3^{2010}.3^9}=\frac{2^{2019}}{3^{2019}}=\left(\frac{2}{3}\right)^{2019}< 1\)

 \(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)

Cách 2 :

Nhận thấy :

• 2⁹ < 3⁹
• 3²⁰¹⁰ > 2²⁰¹⁰

\(\Rightarrow\frac{2^9}{3^{2010}}< \frac{3^9}{2^{2010}}\)