Question

so sánh:

10⁵⁰ và 2¹⁰⁰

Cho X=3+3²+3³+3⁴+...+3^100.Tìm y,biết 2X+3=3^y

Answer 1

10^50=10^50

2^100=(2^2)^50=4^50

Vậy 10^50>2^100

Answer 2

Ta có : X = 3 + 3² + 3³ + 3⁴ +...+ 3¹⁰⁰ 

=> 3X = 3² + 3³ + 3⁴ +...+ 3¹⁰¹

=> 3X - X = 3¹⁰¹ - 3

=> 2X = 3¹⁰¹ - 3

=> 2X + 3 = 3¹⁰¹

=> y = 101

Answer 3

2¹⁰⁰=(2²)⁵⁰=4⁵⁰

Vì 50 = 50 và 10>4 => 10⁵⁰ > 4⁵⁰ => 10⁵⁰ > 2¹⁰⁰.

x=3+3²+3³+3⁴+...+3¹⁰⁰

=> 3x = 3²+3³+3⁴+...+3¹⁰¹

=> 3x - x =  3²+3³+3⁴+...+3¹⁰¹ - (3+3²+3³+3⁴+...+3¹⁰⁰)

=>2x = 3¹⁰¹ - 3

=>2x + 3 = 3¹⁰¹

=> y = 101

Answer 4

\(10^{50}=10^{50}\)

\(2^{100}=\left(2^2\right)^{50}=4^{50}\)

vi \(4< 10\)nen \(4^{50}< 10^{50}\)

vay \(10^{50}>2^{100}\)

Answer 5

Ta có X=3+3²+3³+3⁴+.... +3^100

=> 3X-X=3²+3³+3⁴+...... +3^101

=>2X=3^101-3

=>101=2X+3

=>y=101

Answer 6

        X = 3 + 3² + 3³ + 3⁴ +...+ 3¹⁰⁰ 

=> 3X = 3² + 3³ + 3⁴ +...+ 3¹⁰¹

=> 3X - X = 3¹⁰¹ - 3

=> 2X = 3¹⁰¹ - 3

=> 2X + 3 = 3¹⁰¹

=> y = 101