Bài 1

S₂ = 21 + 23 + 25 + ... + 1001

Số số hạng của S₂:

(1001 - 21) : 2 + 1 = 491

⇒ S₂  = (1001 + 21) . 491 : 2 = 250901

--------

S₄  = 15 + 25 + 35 + ... + 115

Số số hạng của S₄:

(115 - 15) : 10 + 1 = 11

⇒ S₄ = (115 + 15) . 11 : 2 = 715

Bài 2

a) 2x - 138 = 2³.3²

2x - 138 = 8.9

2x - 138 = 72

2x = 72 + 138

2x = 210

x = 210 : 2

x = 105

b) 5.(x + 35) = 515

x + 35 = 515 : 5

x + 35 = 103

x = 103 - 35

x = 78

c) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305

x = 407

d) 20 - [7.(x - 3) + 4] = 2

7(x - 3) + 4 = 20 - 2

7(x - 3) + 4 = 18

7(x - 3) = 18 - 4

7(x - 3) = 14

x - 3 = 14 : 7

x - 3 = 2

x = 2 + 3

x = 5

e) 9ˣ⁻¹ = 9

x - 1 = 1

x = 1 + 1

x = 2

2:

a: \(2x-138=2^3\cdot3^2\)

=>\(2x-138=8\cdot9=72\)

=>2x=138+72=210

=>x=105

b: \(5\cdot\left(x+35\right)=515\)

=>x+35=103

=>x=103-35=68

c: \(814-\left(x-305\right)=712\)

=>x-305=814-712=102

=>x=102+305=407

d: \(20-\left[7\left(x-3\right)+4\right]=2\)

=>7(x-3)+4=18

=>7(x-3)=14

=>x-3=2

=>x=5

e: \(9^{x-1}=9\)

=>x-1=1

=>x=2

f: \(5^{x-2}-3^2=2^4-\left(2^8\cdot2^2-2^{10}\cdot2^2\right)\)

=>\(5^{x-2}-9=16-1024+4096\)

=>\(5^{x-2}=3097\)

=>\(x-2=log_53097\)

=>\(x=2+log_53097\)

a) \(2\left(3x-4\right)=18\Leftrightarrow3x-4=9\)

\(\Leftrightarrow3x=13\Rightarrow x=\frac{13}{3}\)

b) \(\left(105-x\right)\div25=30+1\)

\(\Leftrightarrow105-x=775\)

\(\Leftrightarrow x=-670\)

c) \(2x-138=22.32\)

\(\Leftrightarrow x-69=11.32\)

\(\Leftrightarrow x-69=352\)

\(\Rightarrow x=421\)

d) \(\left(6x-9\right).28=5628\)

\(\Leftrightarrow\left(2x-3\right).84=5628\)

\(\Leftrightarrow2x-3=67\)

\(\Leftrightarrow2x=70\)

\(\Rightarrow x=35\)

e) \(\left(9x+2\right).3=60\)

\(\Leftrightarrow9x+2=20\)

\(\Leftrightarrow9x=18\)

\(\Rightarrow x=2\)

g) \(\left(26-3x\right)\div5+71=75\)\(\Leftrightarrow26-3x=20\)

\(\Leftrightarrow3x=6\)

\(\Rightarrow x=2\)

h) \(5x+1=125\)

\(\Leftrightarrow5x=124\)

\(\Rightarrow x=\frac{124}{5}\)

i) \(\left(x-5\right)\left(2x+8\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\2x+8=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=5\\2x=-8\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-4\end{cases}}\)

a) 2 ( 3x - 4 ) = 18

<=> 3x - 4     = 9

<=> 3x          = 13

<=> x            = \(\frac{13}{3}\)

b) ( 105 - x ) : 25 = 30 + 1

<=> ( 105 - x ) : 25 = 31

<=> 105 - x        = 775

<=> x                 = -670

c) 2x - 138 = 22 . 32

<=> 2x - 138 = 704

<=> 2x          = 842

<=> x            = 421

a) 2 (3x - 4) = 18

          3x - 4 = 18 : 2

          3x - 4 = 9

                3x = 9 + 4

                3x = 13

                  x =\(\frac{13}{3}\)

b) (105 - x) : 25 = 30 + 1

    (105 - x) : 25 = 31

              105 - x = 31 . 25

               105 - x = 775

                   => x = -670

c) 2x - 138 = 22 . 32

    2x - 138 = 704

              2x = 704 + 138

              2x = 842

                x = 842 : 2

                x = 421

d) (6x - 39) . 28 = 5628

              6x - 39 = 5628 : 28

              6x - 39 = 201

                      6x = 201 + 39

                      6x = 240

                        x = 40

e) (9x + 2) . 3 = 60

             9x + 2 = 60 : 3

             9x + 2 = 20

                   9x = 20 - 2

                    9x = 18

                      x = 18 : 2

                      x = 9

g) (26 - 3x) : 5 + 71 = 75

             (26 - 3x) : 5 = 75 - 71

              (26 - 3x) : 5 = 4

                     26 - 3x = 4 . 5

                     26 - 3x = 20

                            3x = 26 - 20

                            3x = 6

                              x = 6 : 3

                               x = 2

h) 5x + 1 = 125

           5x = 125 - 1

           5x = 124

             x = 124 : 5

             x =\(\frac{124}{5}\)= 24,8

i) (x - 5) (2x + 8) = 0

 \(\Rightarrow\orbr{\begin{cases}x-5=0\\2x+8=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\2x=-8\end{cases}\Leftrightarrow}}\orbr{\begin{cases}x=5\\x=-4\end{cases}}\)

Sai thì thôi~

#Học tốt!!!

~NTTH~

a,  2 x . 2 2 = 32

2 x + 2 = 2 5

x + 2 = 5

x = 3

Vậy x = 3

b,  27 . 3 x = 243

3 3 . 3 x = 3 5

3 3 + x = 3 5

x + 3 = 5

x = 2

Vậy x = 2

c,  2 x . 2 4 = 1024

2 x + 4 = 2 10

x + 4 = 10

x = 6

Vậy x = 6

d,  49 . 7 x = 2401

7 2 . 7 x = 7 4

7 2 + x = 7 4

2 + x = 4

x = 2

Vậy x = 2

a,  2 3 x + 5 2 x = 2 5 2 + 2 3 - 33

8x+25x = 33

33x = 33

x = 1

b,  260 : x + 4 = 5 2 3 + 5 - 3 3 2 + 2 2

260:(x+4) = 5.13–3.13

x+4 = 260:26

x+4 = 10

x = 6

c,  720 : [ 41 - 2 x - 5 ] = 2 3 . 5

41–(2x–5) = 720:40

2x–5 = 41–18

2x = 28

x = 14

d,  3 2 - 2 x - 12 + 35 = 5 2 + 279 : 3 2

7(x–12)+35 = 56

7(x–12) = 21

x–12 = 3

x = 15

(2x + 1) : 7 = 2² + 3²

(2x + 1) : 7 = 4 + 9

(2x + 1) : 7 = 13

2x + 1 = 13 . 7

2x + 1 = 91

2x = 91 - 1

2x = 90

x = 90 : 2

x = 45

\((2x+1):7=2^2+3^2\\\Rightarrow (2x+1):7=4+9\\\Rightarrow(2x+1):7=13\\\Rightarrow2x+1=13\cdot7\\\Rightarrow2x+1=91\\\Rightarrow2x=91-1\\\Rightarrow2x=90\\\Rightarrow x=90:2\\\Rightarrow x=45\\Vậy:x=45\)

x = 45