52 \(\times\) ( y : 78) = 3380

          y : 78 =  3380: 52

          y : 78 = 65

         y          = 65 \(\times\) 78

       y = 5070

y: 55 - y + 33 = 76

\(y\) \(\times\) ( \(\dfrac{1}{55}\) - 1) = 76 - 33

y \(\times\) ( \(\dfrac{-54}{55}\) ) = 43

 y                = 43 : (- \(\dfrac{54}{55}\))

y = - \(\dfrac{2365}{54}\)

Chọn B

a: 7x+58=100

nên 7x=42

hay x=6

c: x-56:x=16

nên x-14=16

hay x=30

c)x - 56 : 4  = 16

x - 56       = 16 : 4 

x- 56        = 4

x               =4 + 56

x               = 60 

d)101 + (36 - 4x) = 105 

          (36- 4x ) = 105 - 101 

          36 - 4x = 4

                4x = 36 - 4 

                4x = 32

                  x = 32:4

                  x = 8

a) 58 + 7x = 100

            7x = 100 - 58

            7x = 42

              x = 42 : 7

              x = 6

b) (x - 12) : 12 = 12

              x - 12 = 12 . 12

             x - 12 = 144

                    x = 144 + 12

                    x = 156

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

Ta có: \(100< 5^{2x-1}\le5^6\)

\(\Leftrightarrow5^2< 5^{2x-1}\le5^6\)

\(\Leftrightarrow2x-1\in\left\{3;5\right\}\)

\(\Leftrightarrow2x\in\left\{4;6\right\}\)

hay \(x\in\left\{2;3\right\}\)

Ta có: 100 < 52x – 1 < 56

=> 52 < 100 < 52x-1 < 56

=> 2 < 2x – 1 < 6

=> 2 + 1 < 2x < 6 + 1

=> 3 < 2x < 7

Vì x ∈ N nên suy ra: x ∈ {2; 3} là thỏa mãn.

Ta có 100=5².4

\(\Rightarrow5^3\le5^{2x-1}< 5^6\)

\(\Rightarrow3\le2x-1< 6\)

\(\Rightarrow4\le2x< 7\)

\(\Rightarrow2\le x< 3,5\)

Mà \(x\) là số tự nhiên

\(\Rightarrow x=2\) hoặc \(x=3\)

x ϵ {2;3}

Bài 4:

\(a,2^{30}=\left(2^3\right)^{10}=8^{10};3^{20}=\left(3^2\right)^{10}=9^{10}\\ Vì:8^{10}< 9^{10}\left(Vì:8< 9\right)\Rightarrow2^{30}< 3^{20}\\ b,9^{10}.27^5=\left(3^2\right)^{10}.\left(3^3\right)^5=3^{20}.3^{15}=3^{35}\\ 243^7=\left(3^5\right)^7=3^{35}\\ Vì:3^{35}=3^{35}\Rightarrow243^7=9^{10}.27^5\)

Bài 5:

100< 5^2x-3 < 59

Đề vầy hả em?

a, 2.(x – 5)+7 = 77

<=> 2.(x – 5) = 70 <=> x – 5 = 35 <=> x = 40

b,  x - 1 3 - 3 5 : 3 4 + 2 . 2 3 = 14

<=> x - 1 3 - 3 + 2 4 = 14

<=>  x - 1 3 = 14 + 3 - 16 = 1

<=> x – 1 = 1 <=> x = 2

c,  1 + 2 + 2 2 + 2 3 + . . . + 2 2016 = 2 x - 1 - 1

Đặt: A = 1 + 2 + 2 2 + 2 3 + . . . + 2 2016 => 2A =  2 + 2 2 + 2 3 + . . . + 2 2017

=> 2A – A = ( 2 + 2 2 + 2 3 + . . . + 2 2017 ) – ( 1 + 2 + 2 2 + 2 3 + . . . + 2 2016 )

=> A =  2 2017 - 1

Ta có:  1 + 2 + 2 2 + 2 3 + . . . + 2 2016 = 2 x - 1 - 1 =>  2 2017 - 1 =  2 x - 1 - 1 => x = 2018

d,  5 2 x - 3 - 2 . 5 2 = 5 2 . 3

<=>  5 2 x - 3 = 5 2 . 3 + 5 2 . 2

<=>  5 2 x - 3 = 5 2 . ( 3 + 2 )

<=>  5 2 x - 3 = 5 3

<=> 2x – 3 = 3 => x = 3

\(5^{2x+1}.5^{x+1}=5^{17}\)

\(\Rightarrow5^{2x+1+x+1}=5^{17}\)

\(\Rightarrow5^{3x+2}=5^{17}\)

\(\Rightarrow3x+2=17\)

\(\Rightarrow3x=15\Rightarrow x=5\)