\(\left(\dfrac{1}{4}\right)^{2n}=\left(\dfrac{1}{8}\right)^2\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{2.2n}=\left(\dfrac{1}{2}\right)^{3.2}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{4n}=\left(\dfrac{1}{2}\right)^6\)

\(\Rightarrow4n=6\)

\(\Rightarrow n=\dfrac{6}{4}=\dfrac{3}{2}\)

n = 3/2

Áp dụng công thức tỉ lệ phân số ta có : 

\(\dfrac{a}{b}=\dfrac{c}{d}\)

\(\Rightarrow\dfrac{a^2}{b^2}=\dfrac{c^2}{d^2}=\dfrac{ac}{bd}\)

a) \(A\left(x\right)=3x^3-4x^4-2x^3+4x^4-5x+3\)

\(\Rightarrow A\left(x\right)=-4x^4+4x^4+3x^3-2x^3-5x+3\)

\(\Rightarrow A\left(x\right)=x^3-5x+3\)

\(B\left(x\right)=5x^3-4x^2-5x^3-4x^2-5x-3\)

\(\Rightarrow B\left(x\right)=5x^3-5x^3-4x^2-4x^2-5x-3\)

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

b) \(A\left(x\right)+B\left(x\right)=x^3-5x+3+\left(-8x^2-5x-3\right)\)

\(\Rightarrow A\left(x\right)+B\left(x\right)=x^3-5x+3-8x^2-5x-3\)

\(\Rightarrow A\left(x\right)+B\left(x\right)=x^3-8x^2-5x-5x+3-3\)

\(\Rightarrow A\left(x\right)+B\left(x\right)=x^3-8x^2-10x\)

\(A\left(x\right)-B\left(x\right)=x^3-5x+3-\left(-8x^2-5x-3\right)\)

\(\Rightarrow A\left(x\right)-B\left(x\right)=x^3-5x+3+8x^2+5x+3\)

\(\Rightarrow A\left(x\right)-B\left(x\right)=x^3+8x^2-5x+5x+3+3\)

\(\Rightarrow A\left(x\right)-B\left(x\right)=x^3+8x^2+6\)

1/2 mũ n = 1/2 mũ 6

Vậy x = 6

\(\left(\dfrac{1}{2}\right)^n=\left(\dfrac{1}{8}\right)^2\)

\(=>\left(\dfrac{1}{2}\right)^n=\left[\left(\dfrac{1}{2}\right)^3\right]^2\)

\(=>\left(\dfrac{1}{2}\right)^n=\left(\dfrac{1}{2}\right)^6\)

\(\Rightarrow n=6\)

a) Gọi H là giao điểm đường trung trực của EF và EF

Xét Δ KEF có :

KH là đường trung trực của EF

⇒ KH vừa là đường cao, trung tuyến của Δ KEF

⇒ Δ KEF là tam giác cân tại K

b) Xét Δ vuông DEF có :

\(\widehat{DEF}+\widehat{DFE}=90^o\)

\(\Rightarrow\widehat{DEF}=90^o-\widehat{DFE}\)

\(\Rightarrow\widehat{DEF}=90^o-40^o\)

\(\Rightarrow\widehat{DEF}=50^o\)

mà \(\widehat{DEK}+\widehat{KEF}=\widehat{DEF}\)

     \(\widehat{KEF}=\widehat{DFE}=40^o\) (Δ KEF là tam giác cân tại K)

\(\Rightarrow\widehat{DEK}=\widehat{DEF}-\widehat{KEF}=50^o-40^o=10^o\)

Quãng đường đó thực tế dài là :

\(30.120000=3600000=36.10^5=3,6.10^6\left(cm\right)\)

29) 2.x⁴ = 2.3⁴

x⁴ = 3⁴

x = 3 hoặc x = -3

30) 5.x³ = 5.4³

x³ = 4³

x = 4

31) 7/5 . x⁵ = 7/5 . 4⁵

x⁵ = 4⁵

x = 4

32) 3/4 . x¹² = 3/4 . 5¹²

x¹² = 5¹²

x = 5 hoặc x = -5

33) 9.x⁶ = 9.7⁶

x⁶ = 7⁶

x = 7 hoặc x = -7

34) x⁹ = 2.2⁸

x⁹ = 2⁹

x = 2

35) x¹² = 5⁴.5⁸

x¹² = 5¹²

x = 5 hoặc x = -5

36) 5.3ˣ = 7.3⁵ - 2.3⁵

5.3ˣ = 3⁵.(7 - 2)

5.3ˣ = 5.3⁵

3ˣ = 3⁵

x = 5

37) 9.x⁶ = 6.5⁶ + 3.5⁶

9.x⁶ = (6 + 3).5⁶

9.x⁶ = 9.5⁶

x⁶ = 5⁶

x = 5 hoặc x = -5

38) x¹⁰ = 4.4¹⁰ - 3.4¹⁰

x¹⁰ = (4 - 3).4¹⁰

x¹⁰ = 4¹⁰

x = 4 hoặc x = -4

39) 7.x⁷ = 5.3⁷ + 2.3⁷

7.x⁷ = (5 + 2).3⁷

= 7.x⁷ = 7.3⁷

x⁷ = 3⁷

x = 3

40) 7.x⁸ = 2⁹ + 5.2⁸

7.x⁸ = (2 + 5).2⁸

7.x⁸ = 7.2⁸

x⁸ = 2⁸

x = 2 hoặc x = -2

41) 5.x¹⁰ = 8.3¹⁰ - 3.3¹⁰

5.x¹⁰ = (8 - 3).3¹⁰

5.x¹⁰ = 5.3¹⁰

x¹⁰ = 3¹⁰

x = 3 hoặc x = -3

42) 5.(x + 6)⁵ = 2.3⁵ + 3.3⁵

5.(x + 6)⁵ = (2 + 3).3⁵

5.(x + 6)⁵ = 5.3⁵

(x + 6)⁵ = 3⁵

x + 6 = 3

x = 3 - 6

x = -3

43) (2x + 1)⁸ = 5.9⁷ + 4.9⁷

(2x + 1)⁸ = (5 + 4).9⁷

(2x + 1)⁸ = 9.9⁷

(2x + 1)⁸ = 9⁸

2x + 1 = 9 hoặc 2x + 1 = -9

*) 2x + 1 = 9

2x = 8

x = 4

*) 2x + 1 = -9

2x = -10

x = -5

Vậy x = -5; x = 4

44) (x + 1)³ + 4.(x + 1)³ = 5.3⁶

5(x + 1)³ = 5.(3²)³

(x + 1)³ = 9³

x + 1 = 9

x = 8

45) 1/5 . (x + 2)² + 1/3 . (2x - 2)³ = 1/5 . (x + 2)² + 1/3 . 2³

1/3 . (2x  - 2)³ = 1/3 . 2³

(2x - 2)³ = 2³

2x - 2 = 2

2x = 4

x = 2

46) 2/3 . (2x + 4)² - 1/3 . (x + 1)² = -1/3 . (2x + 4)² + 2/3 (x + 1)²

2/3 (2x + 4)² + 1/3 (2x + 4)² - 1/3 (x + 1)² - 2/3 (x + 1)² = 0

(2x + 4)² - (x + 1)² = 0

(2x + 4)² = (x + 1)²

2x + 4 = x + 1 hoặc 2x + 4 = -x - 1

*) 2x + 4 = x + 1

2x - x = 1 - 4

x = -3

*) 2x + 4 = -x - 1

2x + x = -1 - 4

3x = -5

x = -5/3

Vậy x = -3; x = -5/3

a) \(x^2-\dfrac{4}{3}x=0\)

\(\Rightarrow x\left(x-\dfrac{4}{3}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x-\dfrac{4}{3}=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{3}\end{matrix}\right.\)

b) \(\left|3x+7\right|=5\)

\(\Rightarrow\left[{}\begin{matrix}3x+7=5\\3x+7=-5\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}3x=-2\\3x=-12\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\x=-4\end{matrix}\right.\)

c) \(2\left|7-2x\right|=6\)

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

\(\Rightarrow\left[{}\begin{matrix}7-2x=3\\7-2x=-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}2x=4\\2x=10\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)

d) \(5\left(x+2\right)+2\left(x-1\right)=10\)

\(\Rightarrow5x+10+2x-2=10\)

\(\Rightarrow5x+2x+8=10\)

\(\Rightarrow7x=2\)

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

e) \(6\left(x-3\right)-4\left(x+2\right)=15\)

\(\Rightarrow6x-18-4x-8=15\)

\(\Rightarrow6x-4x-18-8=15\)

\(\Rightarrow2x-26=15\)

\(\Rightarrow2x=41\)

\(\Rightarrow x=\dfrac{41}{2}\)

g) \(\left(12-2x\right)^2=\dfrac{4}{9}\)

\(\Rightarrow\left[{}\begin{matrix}12-2x=\dfrac{2}{3}\\12-2x=-\dfrac{2}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}12x=12-\dfrac{2}{3}\\12x=12+\dfrac{2}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}12x=\dfrac{34}{3}\\12x=\dfrac{38}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{34}{3}.\dfrac{1}{12}\\x=\dfrac{38}{3}.\dfrac{1}{12}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{17}{18}\\x=\dfrac{19}{18}\end{matrix}\right.\)

\(\dfrac{x}{2}=\dfrac{4}{5}=4.2:5=1,6\)

2x​=54​=4.2:5=1,6