Question

1. Tìm x biết:

a, \(\dfrac{3x+2}{5x+1}\) = \(\dfrac{3x-1}{5x+1}\)

b, \(\dfrac{x+1}{2x+1}\) = \(\dfrac{0,5x+2}{x+3}\)

c, \(\dfrac{1}{4}\)x\(\dfrac{2}{6}\)x\(\dfrac{3}{8}\)x\(\dfrac{4}{10}\)x\(\dfrac{5}{12}\)...\(\dfrac{30}{62}\)x\(\dfrac{31}{64}\)= \(2x\)

2. Tìm số nguyên dương n biết:

a, 32\(\le\)2ⁿ\(\le\)128        b, 2 x 16\(\ge\)2ⁿ \(\ge\)4      c, 9 x 27\(\le\) 3ⁿ \(\le\)243

3. So sánh

a, 99²⁰ và 9999¹⁰          b, 3²¹ và 2³¹     c, 2³⁰ + 3³⁰ + 4³⁰  = 3 x 24¹⁰

Answer 1

Bài 2:

a) \(32\le2^n\le128\)

\(\Rightarrow2^5\le2^n\le2^7\\ \Rightarrow5\le n\le7\)

Mà: n ∈ N

`=>n={5;6;7}` 

b) 

\(2\cdot16\ge2^n\ge4\\ \Rightarrow2\cdot2^4\ge2^n\ge2^2\\ \Rightarrow2^5\ge2^n\ge2^2\\ \Rightarrow5\ge n\ge2\)

Mà: n ∈ N

`=>n∈{2;3;4;5}` 

c) 

\(9\cdot27\le3^n\le243\\ \Rightarrow3^2\cdot3^3\le3^n\le3^5\\\Rightarrow 3^5\le3^n\le3^5\)

\(\Rightarrow3^n=3^5\\ \Rightarrow n=5\)