a) \(\frac{x^7}{81}=27\)

=> x⁷ = 27.81

=> x⁷ = 3³.3⁴

=> x⁷ = 3⁷

=> x = 3

Vậy x = 3

b) \(\frac{x^8}{9}=729\)

=> x⁸ = 729.9

=> x⁸ = 3⁶.3²

=> x⁸ = 3⁸ = (-3)⁸

=> \(x\in\left\{3;-3\right\}\)

Vậy \(x\in\left\{3;-3\right\}\)

x^7/81 = 27                                                    x^8/9 = 729

x^7 : 81= 27                                                   x^8  : 9 = 729

x^7       =27.81                                                x^8       = 729.9

x^7        =2187                                                x^8       =6561

x^7        = 3^7                                                  x^8       = 3^8

=> x      =3                                                       => x      = 3

\(\frac{x^7}{81}=27\Rightarrow x^7=27.81=2187\Rightarrow x=\sqrt[7]{2187}=3\)

\(\frac{x^8}{9}=729\Rightarrow x^8=729.9=6561\Rightarrow x=\sqrt[8]{6561}=3\)

\(\frac{x^7}{81}=27\)

\(\Rightarrow x^7.1=81.27\)

\(\Rightarrow x^7=2187\)

Ta thấy : \(3^7=2187\)

\(\Rightarrow x=\sqrt[7]{2187}=3\)

\(\frac{x^8}{9}=729\)

\(\Rightarrow x^8.1=729.9\)

\(\Rightarrow x^8=6561\)

\(\Rightarrow x=\sqrt[8]{6561}=3\)

`Answer:`

\(\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{9}\right)+\left(x+\frac{1}{27}\right)+...+\left(x+\frac{1}{729}\right)=\frac{4209}{729}\)

\(\Leftrightarrow\left(x+\frac{1}{3}\right)+\left(x+\frac{1}{3^2}\right)+\left(x+\frac{1}{3^3}\right)+...+\left(x+\frac{1}{3^6}\right)=\frac{4209}{729}\)

\(\Leftrightarrow6x+\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\right)=\frac{4209}{729}\text{(*)}\)

Đặt \(N=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\)

\(\Leftrightarrow3N=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^5}\)

\(\Leftrightarrow3N-N=\left(1+\frac{1}{3}+\frac{1}{3^2}+..+\frac{1}{3^5}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^6}\right)\)

\(\Leftrightarrow2N=1-\frac{1}{3^6}\)

\(\Leftrightarrow2N=\frac{728}{729}\)

\(\Leftrightarrow N=\frac{364}{729}\)

\(\text{(*)}\Leftrightarrow6x+\frac{364}{729}=\frac{4209}{729}\)

\(\Leftrightarrow6x=\frac{3845}{729}\)

\(\Leftrightarrow x=\frac{3845}{4374}\)

\(\frac{x^7}{81}=27\Rightarrow x^7=27.81\Rightarrow x^7=3^3.3^4\Rightarrow x^7=3^7\Rightarrow x=3\)

\(\frac{x^8}{9}=729\Rightarrow x^8=729.9\Rightarrow x^8=3^6.3^2\Rightarrow x^8=3^8\Rightarrow x=3\)

a) Ta có: \(\frac{x^7}{81}=27\)

\(\Rightarrow x^7=27.81=2187\)

Mà \(2187=3^7\) \(\Rightarrow x^7=3^7\Leftrightarrow x=3\)

Vậy x = 3

b) Ta có: \(\frac{x^8}{9}=729\)

\(\Rightarrow x^8=729.9=6561\)

Mà \(6561=3^8\) \(\Rightarrow x^8=3^8\Leftrightarrow x=3\)

Vậy x = 3

CHÚC BẠN HỌC TỐT

\(\frac{x^7}{81}=27\Rightarrow27.81=x^7\Rightarrow x=3\)

\(\frac{x^8}{9}=729\Rightarrow x^8=729.9\Rightarrow x=3\)

tíc mình

nha

\(a.\)\(\frac{x^7}{81}=27\)

\(\Rightarrow x^7=27.81\)

\(\Leftrightarrow x^7=2187\)

\(\Leftrightarrow x^7=3^7\)

\(\Leftrightarrow x=3\)

\(b.\)\(\frac{x^8}{9}=729\)

\(\Rightarrow x^8=729.9\)

\(\Leftrightarrow x^8=6561\)

\(\Leftrightarrow x^8=3^8\)

\(\Leftrightarrow x=3\)

Vậy : Ở cả 2 câu x đều bằng 3 nhé.

~ Rất vui vì giúp đc bn ~

\(\frac{x^7}{81}\) = 27

x⁷ : 81 = 27

x⁷        = 27 . 81 = 3³ . 3⁴

x⁷         = 3⁷

Suy ra : x = 3

Bài 2 :

   \(\frac{x^8}{9}\) = 729

x⁸ : 9     = 729

x⁸          =  729 . 9

x⁸          =     3⁶ . 3²

x⁸              =              3⁸

Suy ra : x = 3

\(x\) \(\times\) \(\dfrac{1}{4}\) = 6 : 1 : 2

\(x\) \(\times\) \(\dfrac{1}{4}\) = 6:2

\(x\) \(\times\) \(\dfrac{1}{4}\) =  3

\(x\)         = 3 : \(\dfrac{1}{4}\)

\(x\)        = 12

Mình nhầm đoạn 6:1/2.nhờ bạn giải lại hộ mình với

\(x\)\(\times\) \(\dfrac{1}{4}\) = 6 : \(\dfrac{1}{2}\)

\(x\) \(\times\) \(\dfrac{1}{4}\) = 6 \(\times\) \(\dfrac{2}{1}\)

\(x\) \(\times\) \(\dfrac{1}{4}\) = 12

\(x\)       =  12 : \(\dfrac{1}{4}\)

\(x\)      = 48

Tính nhanh:

                         A =         \(\dfrac{2}{3}\) + \(\dfrac{2}{9}\) + \(\dfrac{2}{27}\) + \(\dfrac{2}{81}\) + \(\dfrac{2}{243}\) + \(\dfrac{2}{729}\)

                  A \(\times\) 3 =  2  +  \(\dfrac{2}{3}\) + \(\dfrac{2}{9}\) + \(\dfrac{2}{27}\) + \(\dfrac{2}{81}\) + \(\dfrac{2}{243}\) 

            A \(\times\) 3 - A = 2 - \(\dfrac{2}{729}\)

           A \(\times\) ( 3 - 1) = 2 \(\times\) ( 1 - \(\dfrac{1}{729}\))

             A \(\times\) 2       = 2 \(\times\) \(\dfrac{728}{729}\)

            A = 2 \(\times\) \(\dfrac{728}{729}\) : 2

           A = \(\dfrac{728}{729}\)

c, tính:

 \(\dfrac{4}{5}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{6}\)

= \(\dfrac{4}{5}\) + \(\dfrac{1}{3}\)

= \(\dfrac{17}{15}\)

a) x = 44.             

b) x = 40.            

c) x = 95.             

d) x = 10.

a) x - 120: 30 = 40

    x    -40        =40

              x        =40+40

              x        =80

b) (x + 120) : 20 = 8

    (x+ 120)         = 8x20

     x+120           =160

     x                   = 160-120

     x                  = 40

c) (x + 5). 3 = 300

     x+5=300:3

     x+5=100

     x=100-5

     x=95

d) x.2 + 21 : 3= 27

    x.2   +7=27

      x.2   = 27-7

    x.2= 20

      x=20:2

      x=10