2^x+1 - 2^x = 32

2^x. 2 - 2^x = 32

2^x. (2-1) = 32

2^x = 32

x = 5

Bài 1 :

a) 7^2x-1 = 343

=> 7^2x-1 = 7³

=> 2x - 1 = 3 => 2x = 4 => x = 2

b) (7x - 11)³ = 2⁵.3² + 200

=> (7x - 11)³ = 32.9 + 200

=> (7x - 11)³ = 488

xem kĩ lại đề này :vvv

c) 174 - (2x - 1)² = 5³

=> (2x - 1)² = 174 - 5³

=> (2x - 1)² = 174 - 125 = 49

=> (2x - 1)² = (\(\pm\)7)²

=> \(\orbr{\begin{cases}2x-1=7\\2x-1=-7\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=-3\end{cases}}\)

Mà x \(\in\)N nên x = 4( thỏa mãn điều kiện)

Bài 2 :

a) x⁵ = 32 => x⁵ = 2⁵ => x = 2

b) (x + 2)³ = 27

=> (x + 2)³ = 3³

=> x + 2 = 3 => x = 3 - 2 = 1

c) (x - 1)⁴ = 16

=> (x - 1)⁴ = 2⁴

=> x - 1 = 2 => x = 3 ( vì đề bài cho x thuộc N nên thỏa mãn)

d) (x - 1)⁸ = (x - 1)⁶

=> (x - 1)⁸ - (x - 1)⁶ = 0

=> (x - 1)⁶ [(x - 1)² - 1] = 0

=> \(\orbr{\begin{cases}\left(x-1\right)^6=0\\\left(x-1\right)^2-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\\left(x-1\right)^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\\left(x-1\right)^2=\left(\pm1\right)^2\end{cases}}\)

+) x - 1 = 1 => x = 2 ( tm)

+) x - 1 = -1 => x = 0 ( tm)

Vậy x = 1,x = 2,x = 0

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[(46-32)^2-(54-42)^2]*36-1872

=(14^2-12^2)*36-1872

=(196-144).36-1872

=52.36-1872

=1872-1872

=0

(x-7)^7=(x-7)^8

=>(x-7)^7-(x-7)^8=0

=>(x-7)^7.1-(x-7)^7.(x-7)=0

=>(x-7)^7.[1-(x-7)]=0

\(\Rightarrow\orbr{\begin{cases}x-7=0\\1-\left(x-7\right)=0\end{cases}\Rightarrow\orbr{\begin{cases}x=7;-7\\x=0\end{cases}}}\)

Vậy x={7;-7;0}

1+2^3+3^3-4^2.x=20

=>36-4^2.x=20

=>4^2.x=16=4^2

=>2.x=2

=>x=1

a = 2^x .3^y => số ước tự nhiên của a là (x+1).(y + 1) => (x+1)(y + 1) = 32 = 1.32 = 2.16 = 4.8 = 8.4 = 16.2 = 32.1

Mà x + y = 10 nên (x + 1) + (y + 1) = 12

=> x + 1 = 4; y + 1 = 8 hoặc x+ 1 = 8; y+ 1 = 4

+) x + 1 = 4; y + 1 = 8 => x = 3; y = 7

+) x + 1 = 8; y + 1 = 4 => x = 7; y = 3

Vậy....

bài làm

a = 2^x .3^y =

> số ước tự nhiên của a là (x+1).(y + 1)

=> (x+1)(y + 1) = 32 = 1.32 = 2.16 = 4.8 = 8.4 = 16.2 = 32.1

Do x + y = 10 nên (x + 1) + (y + 1) = 12

=> x + 1 = 4; y + 1 = 8

hoặc x+ 1 = 8; y+ 1 = 4

Đáp số:............

hok tốt

`Answer:`

`\frac{x-1}{34}+\frac{x-2}{34}=\frac{x-3}{32}+\frac{x-4}{31}`

`<=>\frac{x-1}{34}-1+\frac{x-2}{33}-1=\frac{x-3}{32}-1+\frac{x-4}{31}-1`

`<=>\frac{x-35}{34}+\frac{x-35}{33}=\frac{x-35}{32}+\frac{x-35}{31}`

`<=>(x-35)(\frac{1}{34}+\frac{1}{33}-\frac{1}{32}-\frac{1}{31})=0`

`<=>x-35=0`

`<=>x=35`

4) Ta có: \(x\) ⋮ 13 vậy \(x\in B\left(13\right)\)

\(B\left(13\right)=\left\{0;13;26;39;52;65;78;91\right\}\)

Mà: \(20< x< 70\Rightarrow x\in\left\{26;39;52;65\right\}\)

5)

a) Ta có: \(\text{Ư}\left(32\right)=\left\{1;2;4;8;16;32\right\}\)

Vậy ước lớn hơn 4 và nhỏ hơn 17 của 32 là 8;16

b) Bạn viết lại đề

c) Ta có: x ⋮ 6 và 30 ⋮ x

Vậy x thuộc bội của 6 và ước của 30

Mà: \(Ư\left(30\right)=\left\{1;2;3;5;6;10;15;30\right\}\)

\(B\left(6\right)=\left\{0;6;12;18;24;30;36;42;...\right\}\)

\(\Rightarrow x\in\left\{6;30\right\}\)