5³⁰⁰ = (5²)¹⁵⁰ = 25¹⁵⁰

3⁴⁵³ > 3⁴⁵⁰ = (3³)¹⁵⁰ = 27¹⁵⁰

Vì 25¹⁵⁰ < 27¹⁵⁰ < 3⁴⁵³

=> 5³⁰⁰ < 3⁴⁵³

\(5^{300}=\left(5^2\right)^{150}=25^{150}\)

\(3^{453}=\left(3^3\right)^{151}=27^{151}=27.27^{150}\)

Vì    \(25^{150}< 27.27^{150}\)nên  \(5^{300}< 3^{453}\)

3x24^100=(2x3x4)^100 
=3x(3^100)x4^150 
xet 4^300-3x24^100= 
4^300-3x(3^100)x4^150= 
(4^150)(4^150-3x3^100)> 
(4^150)(3^150-3x3^100)> 
(4^150)(3^100)(3^50-3)>0 

==>.....

3^450>5^300

\(5^{300}và3^{450}\\ 5^{300}=15^{327}\\ 3^{450}=15^{445}\)

Vì \(15^{327}< 15^{445}\\ \Rightarrow5^{300}< 3^{450}.\)

5³⁰⁰ = (5²)¹⁵⁰ = 25¹⁵⁰

3⁴⁵⁰ = (3³)¹⁵⁰ = 27¹⁵⁰

Do 25 < 27 nên 25¹⁵⁰ < 27¹⁵⁰

Vậy 5³⁰⁰ < 3⁴⁵⁰

3^450=15^90 và 5^300=15^100

Vì 15^90<15^100 nên 3^450<5^300

 3450=(33)150=27150

5300=(52)150=251505300=(52)150=25150

Do27>25⇒27150>25150⇒3450>530027>25⇒27150>25150⇒3450>5300

Vậy3450>53003450>5300

\(5^{300}=\left(5^3\right)^{100}=125^{100}< 243^{100}=\left(3^5\right)^{100}=3^{500}\)

\(5^{300}=\left(5^3\right)^{100}=125^{100}< 243^{100}=\left(3^5\right)^{100}=3^{500}\)

\(5^{300};3^{500}=125^{100};243^{100}\)

\(\Rightarrow5^{300}< 3^{500}\)

A=3^450=15^90 và B=5^300=15^100

Vì 15^90 <15^100 nên3^450<5^300

Vậy A<B

A=3⁴⁵⁰=(3³)¹⁵⁰=27¹⁵⁰

B=5³⁰⁰=(5²)¹⁵⁰=25¹⁵⁰

Suy ra A=3⁴⁵⁰>B=5³⁰⁰

truong my nhn dung