Question

Bài 1 : So sánh 

a) 10³⁰ và 2¹⁰⁰

b) 2⁹¹ và 5³⁵

c) 2¹⁰⁰⁰ và 5⁴⁰⁰

d) 5³⁰⁰ và 3⁴⁵³

e) 13⁴⁰ và 2¹⁶¹

Answer 1

\(a,10^{30}=\left(10^3\right)^{10}=1000^{10}\)

\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

\(1000^{10}< 1024^{10}\Rightarrow10^{30}< 2^{100}\)

\(b,2^{91}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=\left(5^5\right)^7=3124^7\)

\(8192^7>3124^7\)

\(\Rightarrow2^{91}>5^{35}\)

\(c,2^{1000}=\left(2^{10}\right)^{100}=1024^{100}\)

\(5^{400}=\left(5^4\right)^{100}=625^{100}\)

\(1024^{100}>625^{100}\)

\(\Rightarrow2^{1000}>5^{400}\)

Answer 2

cảm ơn bạn nhiều