\(a,\Rightarrow\dfrac{\left(-3\right)^x}{\left(-3\right)^4}=\left(-3\right)^3\\ \Rightarrow\left(-3\right)^{x-4}=\left(-3\right)^3\\ \Rightarrow x-4=3\Rightarrow x=7\\ b,Sửa:\left(x-\dfrac{1}{2}\right)^2=25\Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=5\\x-\dfrac{1}{2}=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{11}{5}\\x=-\dfrac{9}{5}\end{matrix}\right.\)

a) \(x+\dfrac{4}{9}=\dfrac{5}{27}\)  

    \(x=\dfrac{5}{27}-\dfrac{4}{9}\)

   \(x=-\dfrac{7}{27}\)

b) \(x-\dfrac{4}{11}=\dfrac{7}{33}\)

   \(x=\dfrac{7}{33}+\dfrac{4}{11}\)

   \(x=\dfrac{19}{33}\)

c) \(\dfrac{8}{5}-x=\dfrac{1}{3}\times\dfrac{2}{5}\)

  \(\dfrac{8}{5}-x=\dfrac{2}{15}\)

          \(x=\dfrac{8}{5}-\dfrac{2}{15}\)

          \(x=\dfrac{22}{15}\)

d) \(x-\dfrac{3}{4}=\dfrac{1}{2}+\dfrac{2}{6}\)

   \(x-\dfrac{3}{4}=\dfrac{5}{6}\)

   \(x=\dfrac{5}{6}+\dfrac{3}{4}\)

   \(z=\dfrac{19}{12}\)

Ví dụ : 5/2 = 5 phần 2

a)\(\left(\frac{3}{5}\right)^5\times x=\left(\frac{3}{7}\right)^7\)

\(\Leftrightarrow\frac{3^5}{5^5}\times x=\frac{3^7}{7^7}\)

\(\Leftrightarrow x=\frac{3^7}{7^7}:\frac{3^5}{5^5}\)

\(\Leftrightarrow x=\frac{3^7\times5^5}{7^7\times3^5}\)

\(\Leftrightarrow x=\frac{3^2\times5^5}{7^7}\)

b)\(\left(\frac{-1}{3}\right)^3\times x=\frac{1}{81}\)

\(\Leftrightarrow\frac{\left(-1\right)^3}{3^3}\times x=\frac{1}{3^4}\)

\(\Leftrightarrow x=\frac{1}{3^4}:\frac{-1}{3^3}\)

\(\Leftrightarrow x=\frac{1\times3^3}{3^4\times\left(-1\right)}\)

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

c)\(\Leftrightarrow\left(x-\frac{1}{2}\right)^3=\left(\frac{1}{3}\right)^3\)

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

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

\(\Leftrightarrow x=\frac{5}{6}\)

d)\(\Leftrightarrow\left(x+\frac{1}{2}\right)^4=\left(\frac{2}{3}\right)^4\)

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

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

\(\Leftrightarrow x=\frac{1}{6}\)

Vũ Hồng Linh bạn check lại bài đầu dùm =_=" 

\(\left[-\frac{1}{3}\right]^3\cdot x=\frac{1}{81}\)

\(\Leftrightarrow x=\frac{1}{81}:\left[-\frac{1}{3}\right]^3\)

\(\Leftrightarrow x=\frac{1}{81}:\left[-\frac{1}{27}\right]\)

\(\Leftrightarrow x=\frac{1}{81}\cdot(-27)=-\frac{1}{3}\)

\(\left[x-\frac{1}{2}\right]^3=\frac{1}{27}\)

\(\Leftrightarrow\left[x-\frac{1}{2}\right]^3=\left[\frac{1}{3}\right]^3\)

=> Làm nốt 

Mấy bài kia cũng làm tương tự

1) \(x^2-16=\left(x-4\right)\left(x+4\right)\)

2)\(4a^{201}\)

3)\(x^2-3=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)

4)\(25-9y^2=\left(5-3y\right)\left(5+3y\right)\)

5)\(\left(a+1\right)^2-16=\left(a+1-16\right)\left(a+1+16\right)=\left(a-15\right)\left(a+17\right)\)

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

7) (a+b)²-(a-b)²

= \(\left(a^2+2ab+b^2\right)-\left(a^2-2ab+b^2\right)=4ab\)

8 ) a^2 + 2ax + x^2

= ( a + x )²

9) x^2 - 4x + 4

= ( x-2)²

10) x^2-6xy+9y^2

= (x - 3y )²

11) x^3+8

= (x+2)( x² - 2x + 4 )

12) a^3 + 27b^3

= (a + 3b ) ( a² - 3ab + 9b² )

13) 27x^3 - 1 

= ( 3x -1 ) ( 9x² + 3x +1)

14) 1/8 - b^3

= ( 1/2 - b ) ( 1/4 + 1/2b + b²)

15) a^3 - (a+b)³

= a³ - ( a³ + 3a²b + 3ab² + b³)

= - 3a²b - 3ab²- b³= -b (3a² + 3ab +b²)

16) 4x^2 + 4x + 1

= (2x +1 )²

Từ câu 1 đến câu 16 bạn Minh Anh làm đúng hết rồi, mình chỉ làm các câu còn lại thôi nha.

7 ) ( a + b )² - ( a - b )² = ( a + b + a - b ) .( a + b - a + b ) = 2a.2b = 4ab

8)  a² + 2ax + x² = ( a + x )²

9 ) x² - 4x + 4 = ( x - 2 )²

10 ) x² - 6xy + 9y² = ( x - 3y )²

11 ) x³ + 8 = ( x + 2 ) . ( x² - 2x + 4 )

12 ) a³ + 27b³ = ( a + 3b ) . ( a² - 3ab + 9b² )

13)  27x³ - 1 = ( 3x - 1 ) . ( 9x² + 9x + 1 )

14 ) \(\frac{1}{8}\)- b³ = \(\left(\frac{1}{2}-b\right).\left(\frac{1}{4}+\frac{1}{2}b+b^2\right)\)

15 ) a³ - ( a + b )³ = ( a - a - b ) . [ a² + a. ( a + b ) + ( a + b )² ] 

                             =  - b. ( a² + a² + ab +a² + 2ab + b² )

                             = - b . ( 3a² + 3ab + b² )

16 ) 4x² + 4x + 1 = ( 2x + 1 )²

17 ) ( x + y )² - 2.( x + y ) + 1 = ( x + y - 1 )²

18 ) ( 2x + 3y )² + 2.( 2x + 3y ) + 1 = ( 2x + 3y + 1 )²

a) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)^2=27.\)

\(\Leftrightarrow x^3+27-x\left(x^2-4x+4\right)-27=0.\)

\(\Leftrightarrow x^3-x^3+4x^2-4x=0.\)

\(\Leftrightarrow4x\left(x-1\right)=0.\)

\(\Leftrightarrow\left[{}\begin{matrix}4x=0.\\x-1=0.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0.\\x=1.\end{matrix}\right.\)

Vậy \(S=\left\{0;1\right\}.\)

a) (2^x)⁵ : 4³ = 8¹⁵ => 2^5x = 8¹⁵.4³ = (2³)¹⁵.(2²)³ = 2⁴⁵.2⁶ = 2⁵¹ => 5x = 51 => x = 10,2 

b) (3²)^x .9³ = 243⁹ => 3^2x = 243⁹ : 9³ = (3⁵)⁹ : (3²)³ = 3⁴⁵ : 3⁶ = 3³⁹ => 2x = 39 => x = 19,5

c) (1/125)³.5^x = 25⁵ => 5^x = 25⁵ : (1/125)³ = (5²)⁵ : (1/5³)³ = 5¹⁰ : (5^-3)³ = 5¹⁰ : 5^-9 = 5¹⁹ => x = 19

d) 1/81 : 3^x = 1/729 => 3^x = 1/81 : 1/729 = 1/3⁴.729 = 3^-4.3⁶ = 3² => x = 2

e) (5x - 2)⁴ = 16⁸ = (16²)⁴ = 256⁴

=> 5x - 2 = -256 ; 256 => 5x = -254 ; 258 => x = -50,8 ; 51,6

P/S : Thay x = 10,2 vào câu a , x = 19,5 vào câu b sẽ thấy điều hư cấu : 2^10,2 và 9^19,5.Ko thể tính được giá trị của 2 lũy thừa này.

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