3:

a: 3^x*3=243

=>3^x=81

=>x=4

b; 2^x*16^2=1024

=>2^x=4

=>x=2

c: 64*4^x=16^8

=>4^x=4^16/4^3=4^13

=>x=13

d: 2^x=16

=>2^x=2^4

=>x=4

a,  70 - 5 ( x - 3 ) = 45

⇔ 5 . x - 3 = 70 - 45

⇔ 5 x - 3 = 35

⇔ x - 3 = 35 : 5 ⇔ x - 3 = 7

⇔ x = 10

b,  10 + 2 x = 4 5 : 4 3

⇔ 10 + 2 x = 4 2 ⇔ 10 + 2 x = 16

⇔ 2 x = 4 ⇔ x = 2

c,  60 - 3 x - 2 = 51

⇔ 3 x - 2 = 60 - 51

⇔ 3 x - 2 = 9

⇔ x - 2 = 3 ⇔ x = 5

d,  4 x - 20 = 2 5 : 2 3

⇔ 4 x - 20 = 2 2 ⇔ 4 x - 20 = 4

⇔ 4 x = 24 ⇔ x = 6

1)

a) 2x + 5 = 3⁴ : 3²

2x + 5 = 3²

2x + 5 = 9

2x = 9 - 5

2x = 4

x = 4 : 2

x = 2

b) (3x - 24).73 = 2.74

(3x - 24).73 = 148

3x - 24 = 148/73

3x = 148/73 + 24

3x = 1900/73

x = 1900/73 : 3

x = 1900/219

c) [3.(42 - x)] + 15 = 23.3

126 - 3x + 15 = 69

141 - 3x = 69

3x = 141 - 69

3x = 72

x = 72 : 3

x = 24

d) 126 + (132 - x) = 300

132 - x = 300 - 126

132 - x = 174

x = 132 - 174

x = -42

2)

a) 120 - (x + 55) = 60

x + 55 = 120 - 60

x + 155 = 60

x = 60 - 55

x = 5

b) (7x - 11).3 = 25.52 + 200

(7x - 11).3 = 1500

7x - 11 = 1500 : 3

7x - 11 = 500

7x = 500 + 11

7x = 511

x = 511 : 7

x = 73

c) 2x + 2x + 4 = 544

4x = 544 - 4

4x = 540

x = 540 : 4

x = 135

3) 

a) 10 + 2x = 49 : 47

10 + 2x = 49/47

2x = 49/47 - 10

2x = -421/47

x = -421/47 : 2

x = -421/94

b) 70 - 5(x - 3) = 45

5(x - 3) = 70 - 45

5(x - 3) = 25

x - 3 = 25 : 5

x - 3 = 5

x = 5 + 3

x = 8

c) 4 + 95 : x = 143 : 142 - 23

4 + 95 : x = -3123/142

95 : x = -3123/142 - 4

95 : x = -3691/142

x = 95 : (-3691/142)

x = -13490/3691

a) \(2^x\cdot4=128\)

\(\Rightarrow2^x\cdot2^2=2^7\)

\(\Rightarrow2^{x+2}=2^7\)

\(\Rightarrow x+2=7\)

\(\Rightarrow x=5\)

b) \(\left(2x+1\right)^3=125\)

\(\Rightarrow\left(2x+1\right)^3=5^3\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=4:2\)

\(\Rightarrow x=2\)

c) \(2x-2^6=6\)

\(\Rightarrow2x-64=6\)

\(\Rightarrow2x=70\)

\(\Rightarrow x=70:2\)

\(\Rightarrow x=35\)

d) \(64\cdot4^x=45\)

\(\Rightarrow4^3\cdot4^x=45\)

\(\Rightarrow4^{x+3}=45\)

Xem lại đề

e) \(27\cdot3^x=243\)

\(\Rightarrow3^3\cdot3^x=3^5\)

\(\Rightarrow3^{x+3}=3^5\)

\(\Rightarrow x+3=5\)

\(\Rightarrow x=2\)

g) \(49\cdot7^x=2401\)

\(\Rightarrow7^2\cdot7^x=7^4\)

\(\Rightarrow7^{x+2}=7^4\)

\(\Rightarrow x+2=4\)

\(\Rightarrow x=2\)

h) \(3^x=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

k) \(3^4\cdot3^x=3^7\)

\(\Rightarrow3^{x+4}=3^7\)

\(\Rightarrow x+4=7\)

\(\Rightarrow x=3\)

n) \(3^x+25=26\cdot2^2+2\cdot3^0\)

\(\Rightarrow3^x+25=104+2\)

\(\Rightarrow3^x+25=106\)

\(\Rightarrow3^x=81\)

\(\Rightarrow3^x=3^4\)

\(x=4\)

`@` `\text {Ans}`

`\downarrow`

`a)`

`2^x*4 = 128`

`=> 2^x = 128 \div 4`

`=> 2^x = 2^7 \div 2^2`

`=> 2^x = 2^5`

`=> x = 5`

Vậy, `x = 5.`

`b)`

\(\left(2x+1\right)^3=125\)

`=> (2x + 1)^3 = 5^3`

`=> 2x + 1 = 5`

`=> 2x = 5-1`

`=> 2x = 4`

`=> x = 4 \div 2`

`=> x = 2`

Vậy, `x = 2`

`c)`

\(2x-2^6=6\)

`=> 2x = 6+2^6`

`=> 2x = 70`

`=> x = 70 \div 2`

`=> x = 35`

Vậy, `x = 35`

`d)`

\(64\cdot4^x=45\) Bạn xem lại đề

`e)`

`27*3^x = 243`

`=> 3^3 * 3^x = 3^5`

`=> 3^(3 + x) = 3^5`

`=> 3 + x = 5`

`=> x = 5 - 3`

`=> x = 2`

Vậy, `x = 2`

`g)`

`49* 7^x = 2401`

`=> 7^2 * 7^x = 7^4`

`=> 7^(2 + x) = 7^4`

`=> 2 + x = 4`

`=> x = 4 - 2`

`=> x = 2`

Vậy, `x = 2`

`h)`

`3^x = 81`

`=> 3^x = 3^4`

`=> x = 4`

Vậy, `x = 4`

`k)`

`3^4 * 3^x = 3^7`

`=> 3^(4 + x) = 3^7`

`=> 4 + x = 7`

`=> x = 7 - 4`

`=> x = 3`

Vậy, `x = 3`

`n)`

`3^x + 25 = 26*2^2 + 2*3^0`

`=> 3^x + 25 = 104 + 2`

`=> 3^x + 25 = 106`

`=> 3^x = 106 - 25`

`=> 3^x = 81`

`=> 3^x = 3^4`

`=> x = 4`

Vậy, `x = 4.`

\(#48Cd\)

a) 10+2x=4⁵:4³

10+2x=4²

10+2x=16

2x=16-10

2x=6

  x=6:2

  x=3

vậy x=3

b)130-(100+x)=25

100+x=130-25

100+x=105

       x=105-100

       x=5

vậy x=5

c)2².(x+3²)-5=55

 4.(x+9)=55+5

x+9=60:4

x+9=15

   x=15-9

   x=6

vậy x=9

d)7²-7(13-x)=14

49-7(13-x)=14

7(13-x)=49-14

13-x=35:7

13-x=5

     x=13-5

      x=8

vậy x=8

g) \(\left(2x-1\right)^2-\left(2x+4\right)^2=0\)

\(\Leftrightarrow\left(2x-1+2x+4\right)\left(2x-1-2x-4\right)=0\)

\(\Leftrightarrow-5\left(4x+3\right)=0\)

\(\Leftrightarrow4x+3=0\)

\(\Leftrightarrow4x=-3\)

\(\Leftrightarrow x=\frac{-3}{4}\)

Vậy tập nghiệm của pt là \(S=\left\{\frac{-3}{4}\right\}\)

h) \(\left(2x-3\right)\left(3x+1\right)-x\left(6x+10\right)=30\)

\(\Leftrightarrow3x\left(2x-3\right)+\left(2x-3\right)-6x^2-10x=30\)

\(\Leftrightarrow6x^2-9x+2x-3-6x^2-10x=30\)

\(\Leftrightarrow-9x+2x-3-10x=30\)

\(\Leftrightarrow-17x-3=30\)

\(\Leftrightarrow-17x=33\)

\(\Leftrightarrow x=\frac{-33}{17}\)

Vậy tập nghiệm của pt là \(S=\left\{\frac{-33}{17}\right\}\)

k) \(\left(2x-1\right)\left(8x+5\right)-\left(4x+3\right)^2=20\)

\(\Leftrightarrow8x\left(2x-1\right)+5\left(2x-1\right)-\left(16x^2+24x+9\right)=20\)

\(\Leftrightarrow16x^2-8x+10x-5-16x^2-24x-9=20\)

\(\Leftrightarrow-8x+10x-5-24x-9=20\)

\(\Leftrightarrow-22x-14=20\)

\(\Leftrightarrow-11x-7=10\)

\(\Leftrightarrow x=\frac{-11}{17}\)

Vậy tập nghiệm của pt là \(S=\left\{\frac{-11}{17}\right\}\)

a) \(3^x\cdot3=243\)

\(\Rightarrow3^{x+1}=243\)

\(\Rightarrow3^{x+1}=3^5\)

\(\Rightarrow x+1=5\)

\(\Rightarrow x=4\)

b) \(2^x\cdot162=1024\)

Xem lại đề

c) \(64\cdot4^x=168\)

Xem lại đề

d) \(2^x=16\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)

a: =>3^x=81

=>x=4

b: =>2^x=1024/16^2=4

=>x=2

c: =>4^x=16^8/64=4^16/4^3=4^13

=>x=13

a: \(\Leftrightarrow4^{x-5}\cdot17=68\)

=>4^x-5=4

=>x-5=1

=>x=6

b: \(\Leftrightarrow\dfrac{1}{3}:\left|2x-1\right|=\dfrac{1}{3}+\dfrac{2}{3}=1\)

=>|2x-1|=1/3

=>2x-1=1/3 hoặc 2x-1=-1/3

=>x=2/3 hoặc x=1/3

c: =>|2x-2|=|3x+15|

=>3x+15=2x-2 hoặc 3x+15=-2x+2

=>x=-17 hoặc x=-13/5

a: \(4x^3+12=120\)

=>\(4x^3=108\)

=>\(x^3=27=3^3\)

=>x=3

b: \(\left(x-4\right)^2=64\)

=>\(\left[{}\begin{matrix}x-4=8\\x-4=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=12\\x=-4\end{matrix}\right.\)

c: (x+1)^3-2=5^2

=>\(\left(x+1\right)^3=25+2=27\)

=>x+1=3

=>x=2

d: 136-(x+5)^2=100

=>(x+5)^2=36

=>\(\left[{}\begin{matrix}x+5=6\\x+5=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-11\end{matrix}\right.\)

e: \(4^x=16\)

=>\(4^x=4^2\)

=>x=2

f: \(7^x\cdot3-147=0\)

=>\(3\cdot7^x=147\)

=>\(7^x=49\)

=>x=2

g: \(2^{x+3}-15=17\)

=>\(2^{x+3}=32\)

=>x+3=5

=>x=2

h: \(5^{2x-4}\cdot4=10^2\)

=>\(5^{2x-4}=\dfrac{100}{4}=25\)

=>2x-4=2

=>2x=6

=>x=3

i: (32-4x)(7-x)=0

=>(4x-32)(x-7)=0

=>4(x-8)*(x-7)=0

=>(x-8)(x-7)=0

=>\(\left[{}\begin{matrix}x-8=0\\x-7=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=8\\x=7\end{matrix}\right.\)

k: (8-x)(10-2x)=0

=>(x-8)(x-5)=0

=>\(\left[{}\begin{matrix}x-8=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=5\end{matrix}\right.\)

m: \(3^x+3^{x+1}=108\)

=>\(3^x+3^x\cdot3=108\)

=>\(4\cdot3^x=108\)

=>\(3^x=27\)

=>x=3

n: \(5^{x+2}+5^{x+1}=750\)

=>\(5^x\cdot25+5^x\cdot5=750\)

=>\(5^x\cdot30=750\)

=>\(5^x=25\)

=>x=2