Question

1/ so sánh

a ) 8\(^{12}\)và 12\(^8\)

b)(0,4)\(^{60}\)và (-0,8)\(^{30}\)

c)99\(^{20}\)và 9999\(^{10}\)

d)4\(^{243}\)và 3\(^{324}\)

e)A=\(\frac{20^{15}+1}{20^{16}+1}vàB=\frac{20^{16}+1}{20^{17}+1}\)

Answer 1

1/ so sánh

a) 8¹² và 12⁸

Ta có: \(8^{12}=\left(8^3\right)^4=512^4\\ 12^8=\left(12^2\right)^4=144^4\)

vì 512⁴>144⁴ nên 8¹²>12⁸

b) (0,4)⁶⁰và (-0,8)³⁰

Gọi A= (0,4)⁶⁰ và B= (-0,8)³⁰

\(\Rightarrow\frac{A}{B}=\frac{\left(0,4\right)^{60}}{\left(-0,8\right)^{30}}=\frac{\left(0,1.2^2\right)^{60}}{\left(0,1.2^3\right)^{30}}=\frac{0,1^{60}.2^{120}}{0,1^{30}.2^{90}}=0,1^{30}.2^{30}=0,2^{30}>1\\ \Rightarrow A< B\)

Answer 2

e)\(A=\frac{20^{15}+1}{20^{16}+1}vàB=\frac{20^{16}+1}{20^{17}+1}\\ 20.A=20.\frac{20^{15}+1}{20^{16}+1}=\frac{20^{16}+20}{20^{16}+1}=\frac{20^{16}+1+19}{20^{16}+1}=\frac{20^{16}+1}{20^{16}+1}+\frac{19}{20^{16}+1}=1+\frac{19}{20^{16}+1}\left(1\right)\)

\(20.B=20.\frac{20^{16}+1}{20^{17}+1}=\frac{20^{17}+20}{20^{17}+1}=\frac{20^{17}+1+19}{20^{17}+1}=\frac{20^{17}+1}{20^{17}+1}+\frac{19}{20^{17}+1}=1+\frac{19}{20^{17}+1}\left(2\right)\)

Từ (1) và (2) ⇒ A>B

Answer 3

1)

a) \(8^{12}\) và \(12^8\)

Ta có:

\(8^{12}=\left(8^3\right)^4=512^4.\)

\(12^8=\left(12^2\right)^4=144^4.\)
Vì \(512>144\) nên \(512^4>144^4.\)

=> \(8^{12}>12^8.\)

Chúc bạn học tốt!