\(2^{x+3}-3.2^{x+1}=32\)

<=> 2^x.2^3-3.2^x.2=32

<=> 2^x.(2^3-3.2)=32

<=> 2^x.2=32

<=>2^x=16

<=>2^x=2^4

=>x=4

Vậy...

2^x+3-3.2^x+1=32

= 2^x . 2³ - 3. 2¹ .2^x = 32

2^x . 8 - 6 . 2^x = 32

2^x . (8 - 6 ) = 32

2^x . 2 = 32

2^x+1 = 32

vì 32 = 2⁵ => x + 1=5

                      x = 5-1

                      x = 4

\(2^{x+3}-3.2^{x+1}=32\)

\(2^x.2^3-3.2^x.2=32\)

\(2^x.8-6.2^x=32\)

\(2^x.\left(8-6\right)=32\)

\(2^x.2=32\)

\(2^x=16\)

\(2^x=2^4\)

\(\Rightarrow x=4\)

Bài 3: 

a: Ta có: \(3x^2=75\)

\(\Leftrightarrow x^2=25\)

hay \(x\in\left\{5;-5\right\}\)

b: Ta có: \(2x^3=54\)

\(\Leftrightarrow x^3=27\)

hay x=3

Bài 2: 

b: Ta có: \(30-3\cdot2^n=24\)

\(\Leftrightarrow3\cdot2^n=6\)

\(\Leftrightarrow2^n=2\)

hay n=1

c: Ta có: \(40-5\cdot2^n=20\)

\(\Leftrightarrow5\cdot2^n=20\)

\(\Leftrightarrow2^n=4\)

hay n=2

d: Ta có: \(3\cdot2^n+2^n=16\)

\(\Leftrightarrow2^n\cdot4=16\)

\(\Leftrightarrow2^n=4\)

hay n=2

a) \(2^3.2^2+7^4:7^2\)

\(=2^5+7^2\)

\(=32+49\)

b) \(6^2.47+6^2.53\)

\(=6^2\left(47+53\right)\)

\(=36.100\)

\(=3600\)

\(10+2\cdot x=4^5:4^3\)

\(\Rightarrow10+2\cdot x=4^{5-3}\)

\(\Rightarrow10+2\cdot x=4^2\)

\(\Rightarrow10+2\cdot x=16\)

\(\Rightarrow2\cdot x=16-10\)

\(\Rightarrow2\cdot x=6\)

\(\Rightarrow x=\dfrac{6}{2}=3\)

__________________

\(2\cdot x-6^2:18=3\cdot2^2\)

\(\Rightarrow2\cdot x-36:18=12\)

\(\Rightarrow2\cdot x-2=12\)

\(\Rightarrow2\cdot x=12+2\)

\(\Rightarrow2\cdot x=14\)

\(\Rightarrow x=\dfrac{14}{2}=7\)

_________________

\(70-5\cdot\left(x-3\right)=3\cdot2\)

\(\Rightarrow70-5\cdot\left(x-3\right)=6\)

\(\Rightarrow70-5x+15=6\)

\(\Rightarrow-5x+15=6-70\)

\(\Rightarrow-5x+15=64\)

\(\Rightarrow-5x=64-15\)

\(\Rightarrow-5x=49\)

\(\Rightarrow x=-\dfrac{49}{5}\)

1) \(\dfrac{1}{4}x-\dfrac{1}{3}=\dfrac{-5}{9}\)

\(\Rightarrow\dfrac{1}{4}x=-\dfrac{2}{9}\Rightarrow x=-\dfrac{8}{9}\)

2) \(2^{x-3}-3.2^x=-92\)

\(\Rightarrow2^x\left(2^{-3}-3\right)=-92\)

\(\Rightarrow2^x.\dfrac{-23}{9}=-92\)

\(\Rightarrow2^x=32\Rightarrow x=5\)

a,5.(x-4) mũ 2-7=13

  5.(x-4) mũ 2 =13+7

  5.(x-4) mũ 2 =20

   (x-4) mũ 2 = 20:5

   (x-4)mũ 2= 4

   (x-4) mũ 2=2 mũ 2

    x-4=2

    x=6

   Vậy x = 6

 b, phần này hình như thiếu gì đó

c,2 mũ x+ 3 - 3.2 mũ x+ 1=32

   2 mũ x . 2 mũ 3 - 3 . 2 mũ x . 2 = 32

   2 mũ x . 8 -( 3.2).2 mũ x = 32

   2 mũ x . 8 -6 . 2 mũ x =32 

   2 mũ x .( 8- 6) = 32

   2 mũ x = 32 : 2

   2 mũ x = 16

    2 mũ x=2 mũ 4

   x = 4

   vậy x = 4

  k cho mình nha !!!  

1) \(-\frac{2}{3}\left(x-\frac{1}{4}\right)=\frac{1}{3}\left(2x-1\right)\)

\(-\frac{2}{3}x+\frac{1}{6}=\frac{2}{3}x-\frac{1}{3}\)

\(-\frac{2}{3}x-\frac{2}{3}x=-\frac{1}{3}-\frac{1}{6}\)

\(-\frac{4}{3}x=-\frac{1}{2}\)

\(x=\left(-\frac{1}{2}\right):\left(-\frac{4}{3}\right)\)

\(x=\frac{3}{8}\)

a, 2.3^x = 18

=> 3^x = 9 = 3²

=> x = 2

b, 2^x + 3.2^x + 4.2^x = 32

=> 2^x.(1+3+4) = 32

=> 2^x . 8 = 32

=> 2^x = 4 = 2²

=> x = 2

c, 3^x + 4^x = 5^x

Câu này mik chưa nghĩ ra

a)1.3^x=18

=>3^x=18:2=9

=>3^x=3^2

=>x=2

b)=>2^x.(1+3+4)=32

=>2^x.8=32

=>2^x=4

=>2^x=2^2

=>x=2

2.3^x=18

3x=9

3^x=3²

x=2

2^x+3.2^x+4.2^x=32

2^x(3+4+1)=32

2^x=4

2^x=2²

x=2

7.2^x+1 - 3.2^x+1 = 32

2^x+1 ( 7 - 3 ) = 32

2^x+1 = 8

x+1 = 3

x=2

\(7\times2^{x+1}-3\times2^{x+1}=32\)

\(\Rightarrow2^{x+1}\left(7-3\right)=32\)

\(\Rightarrow2^{x+1}\times4=32\)

\(\Rightarrow2^{x+1}=32\div4\)

\(\Rightarrow2^{x+1}=8\)

\(\Rightarrow2^{x+1}=2^3\)

\(\Rightarrow x+1=3\)

\(\Rightarrow x=3-1\)

\(\Rightarrow x=2\)

7 : 2^x+1 - 3.2^x+1 =32

2^x+1  ( 7 - 3 ) = 32

2^{x + 1} = 8 

x + 1 = 3 

x =2