a) \(\left(\frac{16}{2}\right)^x=2\)

\(8^x=2\)

<=> 2^3x = 2¹

<=> 3x = 1 

=> x = \(\frac{1}{3}\)

b) 8^x : 2^x = 4

(8 : 2)^x = 4

4^x = 4

=> x = 1

c) \(\left(\frac{1}{2}\right)^x=\frac{1}{32}\)

\(\left(\frac{1}{2}\right)^x=\left(\frac{1}{2}\right)^5\)

=> x = 5

\(\left(\frac{16}{2}\right)^x=2\)

\(x=\frac{1}{3}\)

b,\(8^x\div2^x=4\)

\(x=1\)

c,\(\left(\frac{1}{2}\right)^x=\frac{1}{32}\)

\(x=5\)

a)\(16^x=32^8\)

\(\Rightarrow\left(2^4\right)^x=\left(2^5\right)^8\)

\(\Rightarrow2^{4x}=2^{40}\)

\(\Rightarrow4x=40\)

\(\Rightarrow x=10\)

b)\(4^x=32^{40}\)

\(\Rightarrow\left(2^2\right)^x=\left(2^5\right)^{40}\)

\(\Rightarrow2^{2x}=2^{200}\)

\(\Rightarrow2x=200\)

\(\Rightarrow x=100\)

c)\(\left(\dfrac{2}{3}\right)^x=\left(\dfrac{4}{9}\right)^4\)

\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left[\left(\dfrac{2}{3}\right)^2\right]^4\)

\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^8\)

\(\Rightarrow x=8\)

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

\(\Rightarrow2^{3x+1}=\left(2^5\right)^2=2^{10}\)

\(\Rightarrow3x+1=10\)

\(\Rightarrow3x=9\)

\(\Rightarrow x=3\)

e)\(\left(2x-1\right)^3:7=49\)

\(\Rightarrow\left(2x-1\right)^3=343\)

\(\Rightarrow\left(2x-1\right)^3=7^3\)

\(\Rightarrow2x-1=7\)

\(\Rightarrow2x=8\)

\(\Rightarrow x=4\)

a) Ta có: \(16^x=32^8\)

=> \(\left(2^4\right)^x=\left(2^5\right)^8\)

=> \(2^{4.x}=2^{5.8}\)

=> 4x = 40

=> x = 10

Vậy x =10

b) Ta có : \(4^x=32^{40}\)

=> \(\left(2^2\right)^x=\left(2^5\right)^{40}\)

=> \(2^{2x}=2^{5.40}\)

=> 2x = 200

=> x =100

Vậy x = 100

c) Ta có : \(\left(\dfrac{2}{3}\right)^x=\left(\dfrac{4}{9}\right)^4\)

=> \(\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^{2.4}\)

=> x = 8

Vậy x =8

d) Ta có : \(2^{3x+1}=32^2\)

=> \(2^{3x+1}=\left(2^5\right)^2\)

=> 3x+1 =5.2

=> 3x+1 = 10

=> 3x = 10-1=9

=> x= \(\dfrac{9}{3}\)=3

Vậy x = 3

e) (2x-1)\(^3\) : 7 = 49

(2x-1)\(^3\) = 49.7

(2x-1)\(^3\) = 343

(2x-1)\(^3\) = \(7^3\)

=> 2x-1 = 7

2x = 8

x = 8:2

x = 4

Vậy x = 4

bạn có chắc chắn ko???

chịch ko

\(a,x^2=16\)

\(x^2=4^2=\left(-4\right)^2\)

\(x=2\) hoặc \(x=-2\)

\(b,x^3=-8\)

\(x^3=\left(-2\right)^3\)

\(x=-2\)

\(c,\left(x+2\right)^2=4\)

\(\left(x+2\right)^2=2^2=\left(-2\right)^2\)

\(x+2=2\Rightarrow x=0\) hoặc \(x+2=-2\Rightarrow x=-4\)

\(d,\left(1-x\right)^3=1\)

\(1-x=1\)

\(x=0\)

e,phần này mk chưa nghĩ ra,sorry bn nha!

1)))) 4^x=8⁴

(2²)^x=(2³)⁴

2^2x=2¹²

=>2x=12

x=6

2)))) 4^x=32²⁴

(2²)^x=(2⁵)²⁴

2^2x=2¹²⁰

=>2x=120

x=60

3))))8^x=16¹²

(2²)^x=(2⁴)¹²

2^2x=2⁴⁸

=>2x=48

x=24

4))))4^x=8¹²

(2²)^x=(2³)¹²

2^2x=2³⁶

=>2x=36

x=18

tìm số nguyên x

|x|=|14|

1)

2^x=4⁸=2¹⁶

vay x=16

2)

2^x=8^-4=2^-12

=>x=-12

3)

3^x=2¹²/2¹²=1

=>x=0

4)

2^4-x=32⁶.16⁵=2³⁰.2²⁰=2⁵⁰=>4-x=50=>x=-46

I : V~ ảnh

1, 2^x = 4⁸

   2^x = (2²)⁸ 

  2^x = 2¹⁶

2, \(2^x=8^3.\left(\frac{1}{8}\right)^{10}.8^3\)

\(2^x=8^6.\left(\frac{1}{8}\right)^{10}\)

chán qá, ko làm nữa @@

\(\frac{2^{4-x}}{16^5}=32^6\)

=> \(\frac{2^{4-x}}{\left(2^4\right)^5}=\left(2^5\right)^6\)

=> \(\frac{2^{4-x}}{2^{20}}=2^{30}\)

=> \(2^{4-x}=2^{30}.2^{20}\)

=> \(2^{4-x}=2^{50}\)

=> 4  - x = 50

=> x = 4 - 50 = -46

\(\frac{3^{2x+3}}{9^3}=9^{14}\)

=> \(\frac{3^{2x+3}}{\left(3^2\right)^3}=\left(3^2\right)^{14}\)

=> \(\frac{3^{2x+3}}{3^6}=3^{28}\)

=> \(3^{2x+3}=3^{28}.3^6\)

=> \(3^{2x+3}=3^{34}\)

=> 2x + 3 = 34

=> 2x = 34 - 3

=> 2x = 31

=> x = 31/2

a)\(\left|\frac{1}{3}x+\frac{5}{4}\right|-\frac{1}{8}=0\)

\(\Leftrightarrow\left|\frac{1}{3}x+\frac{5}{4}\right|=\frac{1}{8}\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{3}x+\frac{5}{4}=\frac{1}{8}\\\frac{1}{3}x+\frac{5}{4}=-\frac{1}{8}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{27}{8}\\x=-\frac{33}{8}\end{cases}}\)

Vậy x=-27/8 và x=-33/8

b) \(\frac{x-2}{32}=\frac{2}{x-2}\)

\(\Leftrightarrow\left(x-2\right)^2=64\)

\(\Leftrightarrow\left(x-2\right)^2=8^2\)

\(\Leftrightarrow\hept{\begin{cases}x-2=8\\x-2=-8\end{cases}}\Leftrightarrow\hept{\begin{cases}x=10\\x=-6\end{cases}}\)

vậy x=10 hoặc x=-6

a) 23x + 1 = 32x

23x - 32x = -1

-9x = -1

x=-1/-9

x=1/9

b) 3x+2 = 273x-1

3x - 273x = -1 - 2

-270x = -3

x = -3/-270

x=3/270