1.

a) (2x + 1)³ =343

\(\Leftrightarrow\left(2x+1\right)^3=7^3.\)

\(\Leftrightarrow2x+1=7\Rightarrow x=3\)

b) 720 [ 41 (2x - 5)] = 2³ . 5

\(\Leftrightarrow720\left[41\left(2x-5\right)\right]=40\)

\(\Leftrightarrow41\left(2x-5\right)=\frac{40}{720}=\frac{1}{18}\)

\(\Leftrightarrow2x-5=\frac{1}{738}\)

\(\Leftrightarrow2x=\frac{3691}{738}\Leftrightarrow x=\frac{3691}{1476}\)

( 3. x + 1 )³ = 343

( 3. x + 1 )³ = 7³

=> 3x + 1 = 7

=> 3x = 6

=> x = 2

(2x + 1)³ = 343

=> (2x + 1)³ = 7³

=> 2x + 1 = 7

=> 2x = 6

=> x = 3

︵✰ŦO꙰rᎬv̤̈єŕ๑A͙ʟ0ɲéȸ

Forever Alone

(2x + 1)³ = 7³

\(\Rightarrow\)2x + 1 = 7

2x = 7 - 1

2x = 6

  x = 6 : 2

  x = 3

(2x+1)3=343(2x+1)3=343

⇔(2x+1)3=73⇔(2x+1)3=73

⇔2x+1=7⇔2x+1=7

⇔2x=6⇔2x=6

⇔x=3

a: \(\Leftrightarrow2< x< =5\)

hay \(x\in\left\{3;4;5\right\}\)

Bài 3:

x-1 thuoc Ư(4)={1;2;4}

TH1: x-1=1                   TH2: x-1=2

          x=2                             x=3

TH3: x-1=4

           x=5

=>x thuộc {2;3;5}

x-1 thuộc ước của 24

=>Ư(24)={1;2;3;4;6;8;12;24}

=>a-1={1;2;3;4;6;8;12;24}

=>a={2;3;4;5;7;9;13;25}

a,(2x+1)(y-3)=12

2x+1 và y-3 Ư(12)=

=>x=0,y=15

c) Ta có: \(36^{25}=\left(6^2\right)^{25}=6^{50}\)

\(25^{36}=\left(5^2\right)^{36}=5^{72}\)

Ta có: \(6^{50}=\left(6^5\right)^{10}=7776^{10}\)

mà \(5^{70}=\left(5^7\right)^{10}=78125^{10}\)

nên \(6^{50}< 5^{70}\)

mà \(5^{70}< 5^{72}\)

nên \(6^{50}< 5^{72}\)

hay \(36^{25}< 25^{36}\)

a/

Với $x,y$ là số tự nhiên $2x+1, y-3$ là số nguyên. Mà $(2x+1)(y-3)=12$ nên $2x+1$ là ước của 12. 

$2x+1>0, 2x+1$ lẻ nên $2x+1\in \left\{1;3\right\}$

Nếu $2x+1=1\Rightarrow y-3=12$

$\Rightarrow x=0; y=15$

Nếu $2x+1=3\Rightarrow y-3=4$

$\Rightarrow x=1; y=7$ 

Vậy...........

b/

$2^x+2^{x+1}+2^{x+2}+...+2^{x+2015}=2^{2019}-8$

$2^x(1+2+2^2+2^3+...+2^{2015})=2^{2019}-8(1)$
$2^x(2+2^2+2^3+2^4+...+2^{2016})=2^{2020}-16(2)$ (nhân 2 vế với 2)

Lấy (2) trừ (1) theo vế thì:

$2^x(2^{2016}-1)=2^{2020}-2^{2019}-8$

$2^x(2^{2016}-1)=2^{2019}(2-1)-8=2^{2019}-8$

$2^x(2^{2016}-1)=2^3(2^{2016}-1)$

$\Rightarrow 2^x=2^3$

$\Rightarrow x=3$

c/

$25^{36}=(5^2)^{36}=5^{72}$

$36^{25}=(6^2)^{25}=6^{50}=(6^5)^{10}< (5^7)^{10}=5^{70}< 5^{72}$

$\Rightarrow 25^{36}> 36^{25}$

x² = 169 = 13²

x = 13

(2x + 1)³ = 343 = 7³

2x + 1 = 7

2x = 6

x = 3

(x-1)⁵ = 1

(x-1) = 1

x = 2