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Bài 5.5:

\(\left(2x-3\right)\left(x+1\right)+\left(4x^3-6x^2-6x\right):\left(-2x\right)=18\)

\(\Leftrightarrow\left(2x^2+2x-3x-3\right)+2x\cdot\left(2x^2-3x-3\right):\left(-2x\right)=18\)

\(\Leftrightarrow2x^2-x-3-2x^2+3x+3=18\)

\(\Leftrightarrow2x=18\)

\(\Leftrightarrow x=\dfrac{18}{2}\)

\(\Leftrightarrow x=9\) 

1) 

a) 63 : 3² + 7 . 2³

= 63 : 9 + 7 . 4 

= 7 + 7 . 4 

= 7 + 28 

= 35

b) 2³ . 15 - [ 115 - 15 . ( 13 - 11 )² ] 

= 8 . 15 - [ 115 - 15 . 2² ] 

= 8 . 15 - [ 115 - 15 . 4 ] 

= 8 . 15 - [ 115 - 60 ] 

= 8 . 15 - 55

= 120 - 55 

= 65 

c) 53 . 46 + 54 . 74 - 54 . 21 

= 53 . 46 + 54 . ( 74 - 21 ) 

= 53 . 46 + 54 . 53 

= 53 . ( 46 + 54 ) 

= 53 . 100

= 5300

2) 

a) 3x - 5 = 2 

3x = 2 + 5 

3x = 7 

x = 7 : 3 

x = 2,33333....33 ( có 11 chữ số 3 nhưng 2,3333...33 không phải là số tự nhiên ) 

b) 46 + 6 ( x - 5 ) = 52 

6 ( x - 5 ) = 52 - 46 

6 ( x - 5 ) = 6

x - 5 = 6 : 6 

x - 5 = 1 

x = 1 + 5 

x = 6 

Bài 2

a 3x-5=2

=> 3x=7

=> x=7/3

b 46+6(x-5)=52

=> 6(x-5)=6

=> x-5=1

=> x=6 ( tick nhé )

1: =>3^x=81

=>x=4

2: =>2^x=8

=>x=3

3: =>x^3=2^3

=>x=2

4: =>x^20-x=0

=>x(x^19-1)=0

=>x=0 hoặc x=1

5: =>2^x=32

=>x=5

6: =>(2x+1)^3=9^3

=>2x+1=9

=>2x=8

=>x=4

7: =>x^3=115

=>\(x=\sqrt[3]{115}\)

8: =>(2x-15)^5-(2x-15)^3=0

=>(2x-15)^3*[(2x-15)^2-1]=0

=>2x-15=0 hoặc (2x-15)^2-1=0

=>2x-15=0 hoặc 2x-15=1 hoặc 2x-15=-1

=>x=15/2 hoặc x=8 hoặc x=7

1. Tìm số tự nhiên x biết:

1) \(3^x.3=243\)

\(3^x=243:3\)

\(3^x=81\)

\(3^x=3^4\)

\(\Rightarrow x=4\)

_____

2) \(7.2^x=56\)

\(2^x=56:7\)

\(2^x=8\)

\(2^x=2^3\)

\(\Rightarrow x=3\)

_____

3) \(x^3=8\)

\(x^3=2^3\)

\(\Rightarrow x=3\)

_____

4) \(x^{20}=x\)

\(x^{20}-x=0\)

\(x\left(x^{19}-1\right)=0\)

\(\Rightarrow x=0\) hoặc \(x=1\)

5) \(2^x-15=17\)

\(2^x=17+15\)

\(2^x=32\)

\(2^x=2^5\)

\(\Rightarrow x=5\)

_____

6) \(\left(2x+1\right)^3=9.81\)

\(\left(2x+1\right)^3=729=9^3\)

\(\rightarrow2x+1=9\)

\(2x=9-1\)

\(2x=8\)

\(x=8:2\)

\(\Rightarrow x=4\)

_____

7) \(x^6:x^3=125\)

\(x^3=125\)

\(x^3=5^3\)

\(\Rightarrow x=5\)

_____

8) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)

\(\rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)

\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=7\\x=8\end{matrix}\right.\)

_____

9) \(3^{x+2}-5.3^x=36\)

\(3^x.\left(3^2-5\right)=36\)

\(3^x.\left(9-5\right)=36\)

\(3^x.4=36\)

\(3^x=36:4\)

\(3^x=9\)

\(3^x=3^2\)

\(\Rightarrow x=2\)

_____

10) \(7.4^{x-1}+4^{x+1}=23\)

\(\rightarrow7.4^{x-1}+4^{x-1}.4^2=23\)

\(4^{x-1}.\left(7+4^2\right)=23\)

\(4^{x-1}.\left(7+16\right)=23\)

\(4^{x-1}.23=23\)

\(4^{x-1}=23:23\)

\(4^{x-1}=1\)

\(4^{x-1}=4^1\)

\(\rightarrow x-1=0\)

\(x=0+1\)

\(\Rightarrow x=1\)

Chúc bạn học tốt

7 . 2 ^x = 2 ⁹ + 5 . 2 ⁸

7 . 2 ^x =  2 ⁸ . ( 2 + 5 )

7 . 2 ^x = 2 ⁸ . 7

=> 2 ^x  = 2 ⁸

=> x = 8

Tìm số tự nhiên x,biết: 7.2^x=2⁹+5.2⁸

\(7.2^x=1792\)

\(2^x=1792:7=256\)

\(2^x=2^8\)

x=8

bấm **** nha

\(a.\dfrac{3^{27}}{9^6.3^{16}}=\dfrac{3^{27}}{3^{12}.3^{16}}=\dfrac{3^{27}}{3^{28}}=\dfrac{1}{3}\)

\(\left(x-\dfrac{5}{2}\right)^2=\dfrac{9}{4}\\ \Rightarrow x-\dfrac{5}{2}=\pm\dfrac{3}{2}\)

\(TH1:x-\dfrac{5}{2}=\dfrac{3}{2}\Rightarrow x=\dfrac{3}{2}+\dfrac{5}{2}=\dfrac{8}{2}=4\)

\(TH2:x-\dfrac{5}{2}=-\dfrac{3}{2}\Rightarrow x=-\dfrac{3}{2}+\dfrac{5}{2}=\dfrac{2}{2}=1\)

a: \(=\dfrac{3^{27}}{3^{12}\cdot3^{16}}=\dfrac{1}{3}\)

1/ 15 - 3(x + 2) = 3

=> 3(x + 2) = 15 - 3

=> 3(x + 2) = 12

=> x + 2 = 12 : 3 

=> x + 2 = 4

Vậy x = 2

2/ 17.6 + 80.6 + 6.3

= 6 (17 + 80 + 3) 

= 6 . 100 

= 600

câu 1 15-3.(x+2)=3

3.(x+2)=15-3

3.(x+2)=12

x+2=12:3

x+2=4

x=4-2

x=2

Câu 2 17.6 + 80.6 + 6.3

= 6. (17+3+80)

=6. 100

= 600

Câu 3 3².5 + 7.2 - 2³.5

=9.5 + 7.2 - 8.5

= 45+ 14 - 40

=59 -40

=19