Question

So sanh

a) \(2^{225}va3^{150}\)

b) \(2^{92}va3^{25}\)

c) \(9^{20}va9999^{10}\)

Answer 1

a) Ta có:\(2^{225}=2^{9^{25}}=512^{25}\)

\(3^{150}=3^{6^{25}}=729^{25}\)

Vì 512²⁵<729²⁵ nên 2²²⁵<3¹⁵⁰

b) Ta có:

Ta có: \(2^{92}>2^{91}=2^{13^7}=8192^7\)

\(3^{25}< 3^{35}=3^{5^7}=243^7\)

Vì 8192⁷>243⁷ nên 2⁹²>3³⁵

c)Ta có: \(9^{20}=9^{2^{10}}=81^{10}\)

Vì 81¹⁰<9999¹⁰=>9²⁰<9999¹⁰

Answer 2

a) 2²²⁵ = (2³)⁷⁵ = 8⁷⁵ < 9⁷⁵ = (3²)⁷⁵ = 3¹⁵⁰. Vậy 2²²⁵ < 3¹⁵⁰ .

b) 2⁹² = (2²)⁴⁶ = 4⁴⁶ > 3⁴⁶ > 3²⁵. Vậy 2⁹² > 3²⁵.

c) 9²⁰ = (9²)¹⁰ = 81¹⁰ < 9999¹⁰ . Vậy 9²⁰ < 9999¹⁰ .