Bài 3:

Ta có:

`2^1000=(2^5)^200=32^200`

`5^400=(5²)^200=10^200`

Vì `32>10` nên `32^200>10^200`

`⇒2^1000>5^400`

Vậy `2^1000>5^400`

Bài 4:

`a)2^n .8=512`

`⇒2^n .2³=2^9`

`⇒n.3=9`

`⇒n=9:3`

`⇒n=3`

`b)(2n+1)³=729`

`⇒(2n+1)³=9³`

`⇒2n+1=9`

`⇒2n=9-1`

`⇒2n=8`

`⇒n=8:2`

`⇒n=4`

Bài 5:

`a)3^9 :3^7 +5.2²`

`=3²+5.4`

`=9+20`

`=29`

`b)2³.3²-5^16 :5^14`

`=8.9-5²`

`=72-25`

`=47`

`c)(4^7 .3^4 .9^6)/(6^13)`

`=[(2²)^7 .3^4 .(3²)^6]/[(2.3)^13]`

`=(2^14 .3^4 .3^12)/(2^13 .3^13)`

`=2.3³`

`=2.27`

`=54`

Luyện tập

`1.`

`a)1440:[41-(2x-5)]=2^4 .3`

    `1440:[41-(2x-5)]=16.3`

    `1440:[41-(2x-5)]=48`

               `41-(2x-5)=1440:48`

               `41-(2x-5)=30`

                      `2x-5=41-30`

                      `2x-5=11`

                          `2x=11+5`

                          `2x=16`

                            `x=16:2`

                            `x=8`

`b)5.[225-(x-10)]-125=0`

     `5.[225-(x-10)]=0+125`

     `5.[225-(x-10)]=125`

          `225-(x-10)=125:5`

          `225-(x-10)=25`

                    `x-10=225-25`

                    `x-10=200`

                          `x=200+10`

                          `x=210`

`2.`

`a)[545-(45+4.25)]:50-2000:250+2^15 :2^13`

`=[545-(45+100)]:50-8+2²`

`=(545-145):50-8+4`

`=400:50-8+4`

`=8-8+4`

`=0+4`

`=4`

`b)[504-(25.8+70)]:9-15+19^0`

`=[504-(200+70)]:9-15+1`

`=[504-270]:9-15+1`

`=234:9-15+1`

`=26-15+1`

`=11+1`

`=12`

`c)5.{26-[3.(5+2.5)+15]:15}`

`=5.{26-[3.(5+10)+15]:15}`

`=5.{26-[3.15+15]:15}`

`=5.{26-[45+15]:15}`

`=5.{26-60:15}`

`=5.{26-4}`

`=5.22`

`=110`

`d)[1104-(25.8+40)]:9+3^16 :3^12`

`=[1104-(200+40)]:9+3^4`

`=[1104-240]:9+81`

`=864:9+81`

`=96+81`

`=177`

`3.`

`a)(x-15):5+22=24`

    `(x-15):5=24-22`

    `(x-15):5=2`

         `x-15=2.5`

         `x-15=10`

               `x=10+15`

               `x=25`

`b)42-(2x+32)+12:2=6`

    `42-(2x+32)+6=6`

         `42-(2x+32)=6-6`

         `42-(2x+32)=0`

                 `2x+32=42-0`

                 `2x+32=42`

                        `2x=42-32`

                        `2x=10`

                           `x=10:2`

                           `x=5`

`c)134-2{156-6.[54-2.(9+6)]}.x=86`

    `134-2{156-6.[54-2.15]}.x=86`

    `134-2{156-6.[54-30]}.x=86`

    `134-2{156-6.24}.x=86`

    `134-2{156-144}.x=86`

    `134-2.12.x=86`

    `134-24.x=86`

            `24.x=134-86`

            `24.x=48`

                 `x=48:24`

                 `x=2`

Bài 3: So sánh: 2^1000 và 5^400

ta có 2^1000= (2^5)^200 = 32^200

         5^400= (5^2)^200= 25^200 

vì 32>25 nên 32^200 > 25^200

=> 2^1000 > 5^400

Bài 4: Tìm n e N, biết:

a) 2^n. 8 = 512

b) (2n + 1)^3 = 729

giải :

a) 2^n. 8 = 512

= 2^n = 64

= 2^n = 2^6

=> n = 6

b) (2n + 1)^3 = 729

= 2n + 1 = 9

= 2n = 9 - 1

= 2n = 8

= n = 8 : 2

=> n = 4

Bài 5: Tính giá trị biểu thức:

a, 3^9 : 3^7 + 5 . 2^2

= 3^9 - 7 + 5. 4

= 3^2 + 20

= 9 + 20

= 29

b, 2^3 . 3^2 - 5^16 : 5^14

= 8 . 9 - 5^16-14

= 72 - 5^2

= 47

c, 4^7 . 3^4 . 9^6/ 6^13

= (2^2)^7 . 3^4 . (3^2) ^6/ (3 . 2) ^13

= 2^14 . 3^4 . 3^12 / 3^13 . 2^13

= 2 . 3^3 

= 54

Luyện Tập

Bài 1

a) 1440:[ 41− ( 2x−5 ) ] = 2^4.3

= 1440: [ 41 −( 2x− 5 ) ] = 16 .3 = 48

= 41 − (2x−5) =1440 : 48 = 30

= 2x−5 = 41−30 = 11

= 2x = 11+5 = 16

= x=16 : 2

=> x = 8

b) 5. [225 − (x−10)] −125 =0

= 5. [225 − (x−10)] = 0+125 = 125

= 225 − (x−10) = 125 : 5 = 25

= x−10 = 225 - 25 = 200

= x = 200 + 10

=> x = 210

Bài 2:

a) [ 545 − (45 + 4.25) ] :50 − 2000 : 250 + 2^15 : 2^13

= [ 545 − (45 + 4.25) ] : 50 = 8 + 4

= 400 : 50 − 8+4

= 8 − 8+4

=> 4 

b) [ 504 − (25.8+70) ] : 9 − 15 +19^0

= [ 504 −(200 +70) ] :9 −15+1

= [ 504 − 270] : 9 −15+1

= 234 : 9 − 15+1

= 26 − 15 +1

= 11 + 1

= 12

c, 5. {26 − [3. (5+2.5) +15 ] :15}

= 5. { 26 −[ 3. (5+10)+15]:15}

= 5. {26− [3.15 +15] :15}

= 5.{ 26− [45+15] :15}

= 5. {26−60 :15}

= 5. {26 −4}

= 5. 22

= 110

d) [1104− (25.8+40)] :9 + 3^16 :3^12

= [1104 − (200+40)] :9 +3^4

= [1104− 240]:9+81

= 864 :9 +81

= 96 +81

= 177

Bài 3:

a, (x−15):5+22=24

= (x−15):5=24−22 = 2

= x−15=2.5= 10

= x = 10 + 15

=> x = 25

b) 42− (2 x + 32) +12 :2 =6

= 42− (2x + 32) +6 =6

= 42−(2x + 32) = 6-6 = 0

= 2x +32 = 42 − 0 = 42

= 2x = 42−32 = 10

= x = 10 : 2

=> x = 5

c, 134 − 2 {156 − 6. [54 − 2 . (9+6) ] } . x =86

= 134 −2 {156 − 6. [54 − 2.15]} .x =86

= 134 − 2 {156 − 6. [54 − 30]} .x =86

= 134 − 2 {156 − 6.24} .x =86

= 134 − 2 {156 − 144 } .x =86

= 134 − 2.12 .x =86

= 134 − 24 .x =86

= 24.x=134−86 = 48

= x = 48 :24 

=> x = 2