a.(3^2+4^2).x=10^2

(9+16).x     =100

25.x           =100

x                =100:25

x                =4

b.(x-5)^2       =81

x-5             =9

x                =9+5

x                =14

c.(2x+1)^3 = 343

2x+1          = 7

2x              =7-1

2x              =6

x                =6:2

x                = 3

(9+16).x=100

25.x=100

x=100:25

x=4

Ư ( -2 ) \(\in\){ 1 ; -1 ; 2 ; -2 }

Ư ( 4 ) \(\in\){ 1 ; 2 ; 4 }

Ư ( 13 ) \(\in\){ 1 ; 13 }

Ư ( 25 ) \(\in\) { 1; 5 ; 25 }

Ư ( 1 ) \(\in\){ 1 }

Bài 2 :

x - 3 \(\in\){ 1 ; 13 }

x \(\in\){ 4 ; 17 }

x^2-7 \(\in\)Ư ( x^{2 + 2} )

a)\(x^{15}=x\Rightarrow x\in\left\{0;1\right\}\)                                            d)Là ý b

b)\(\left(2x+1\right)^3=125\\ \left(2x+1\right)^3=5^3\Rightarrow2x+1=5\\ 2x=4\\ x=2\)                       e)\(\left(x-3\right)^2=25\\ \Rightarrow\left(x-3\right)^2=5^2\\ \Rightarrow\hept{\begin{cases}x-3=5\Rightarrow x=8\\x-3=-5\Rightarrow x=-2\end{cases}}\)

c)\(\left(x-5\right)^4=\left(x-5\right)^6\\ \Rightarrow x-5\in\left\{0;1\right\}\Rightarrow x\in\left\{5;6\right\}\)

1) + S = 5 + 5² + 5³ + ... + 5⁹⁶ (có 96 số; 96 chia hết cho 6)

S = (5 + 5² + 5³ + 5⁴ + 5⁵ + 5⁶) + (5⁷ + 5⁸ + 5⁹ + 5¹⁰ + 5¹¹ + 5¹²) + ... + (5⁹¹ + 5⁹² + 5⁹³ + 5⁹⁴ + 5⁹⁵ + 5⁹⁶)

S = (5 + 5⁴) + (5² + 5⁵) + (5³ + 5⁶) + (5⁷ + 5¹⁰) + ... + (5⁹³ + 5⁹⁶)

S = 5.(1 + 5³) + 5².(1 + 5²) + 5³.(1 + 5³) + 5⁷.(1 + 5³) +  ... + 5⁹³.(1 + 5³)

S = 5.126 + 5².126 + 5³.126 + 5⁷.126 + ... + 5⁹³.126

S = 126.(5 + 5² + 5³ + 5⁷ + ... + 5⁹³) chia hết cho 126

+ Do 5 + 5² + 5³ + 5⁷ + ... + 5⁹³ chia hết cho 5 mà 126 chia hết cho 2

=> S chia hết cho 10 => S có tận cùng là 0

2) 16²⁰⁰⁸ - 8²⁰⁰⁰

= (...6) - (8⁴)⁵⁰⁰

= (...6) - (...6)⁵⁰⁰

= (...6) - (...6)

= (...0) chia hết cho 10

3) 1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ + 9³ + 10³ = (x + 1²)²

=> 1 + 8 + 27 + 64 + 125 + 216 + 343 + 512 + 729 + 1000 = (x + 1)²

=> (1 + 729) + (8 + 512) + (27 + 343) + (64 + 216) + 125 + 1000 = (x + 1)²

=> 730 + 520 + 370 + 280 + 1125 = (x + 1)²

=> (730 + 370) + (520 + 280) + 1125 = (x + 1)²

=> 1100 + 800 + 1125 = (x + 1)² 

=> 3025 = (x + 1)², vô lí

1) + S = 5 + 5² + 5³ + ... + 5⁹⁶ (có 96 số; 96 chia hết cho 6)

S = (5 + 5² + 5³ + 5⁴ + 5⁵ + 5⁶) + (5⁷ + 5⁸ + 5⁹ + 5¹⁰ + 5¹¹ + 5¹²) + ... + (5⁹¹ + 5⁹² + 5⁹³ + 5⁹⁴ + 5⁹⁵ + 5⁹⁶)

S = (5 + 5⁴) + (5² + 5⁵) + (5³ + 5⁶) + (5⁷ + 5¹⁰) + ... + (5⁹³ + 5⁹⁶)

S = 5.(1 + 5³) + 5².(1 + 5²) + 5³.(1 + 5³) + 5⁷.(1 + 5³) +  ... + 5⁹³.(1 + 5³)

S = 5.126 + 5².126 + 5³.126 + 5⁷.126 + ... + 5⁹³.126

S = 126.(5 + 5² + 5³ + 5⁷ + ... + 5⁹³) chia hết cho 126

+ Do 5 + 5² + 5³ + 5⁷ + ... + 5⁹³ chia hết cho 5 mà 126 chia hết cho 2

=> S chia hết cho 10 => S có tận cùng là 0

a) \(5\left(x+7\right)-10=2^3\cdot5\)

\(\Rightarrow5\left(x+7\right)-10=40\)

\(\Rightarrow5\left(x+7\right)=40+10\)

\(\Rightarrow x+7=\dfrac{50}{5}\)

\(\Rightarrow x+7=10\)

\(\Rightarrow x=10-7\)

\(\Rightarrow x=3\)

b) \(9x-2\cdot3^2=3^4\)

\(\Rightarrow9x-18=81\)

\(\Rightarrow9x=81+18\)

\(\Rightarrow9x=99\)

\(\Rightarrow x=\dfrac{99}{9}\)

\(\Rightarrow x=11\)

c) \(5^{25}\cdot5^{x-1}=5^{25}\)

\(\Rightarrow5^{x-1}=5^{25}:5^{25}\)

\(\Rightarrow5^{x-1}=1\)

\(\Rightarrow5^{x-1}=5^0\)

\(\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

a) $5\left(x+7\right)-10=2^3\cdot 5$

$\Rightarrow 5\left(x+7\right)-10=40$

$\Rightarrow 5\left(x+7\right)=40+10$

$\Rightarrow x+7=\genfrac{}{}{0ex}{}{50}{5}$

$\Rightarrow x+7=10$

$\Rightarrow x=10-7$

$\Rightarrow x=3$

b) $9x-2\cdot 3^2=3^4$

$\Rightarrow 9x-18=81$

$\Rightarrow 9x=81+18$

$\Rightarrow 9x=99$

$\Rightarrow x=\genfrac{}{}{0ex}{}{99}{9}$

$\Rightarrow x=11$

c) $5^{25}\cdot 5^{x-1}=5^{25}$

$\Rightarrow 5^{x-1}=5^{25}:5^{25}$

$\Rightarrow 5^{x-1}=1$

$\Rightarrow 5^{x-1}=5^0$

$\Rightarrow x-1=0$

$\Rightarrow x=1$

mong các bn giúp mình gấp ạ ^^

  Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)