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

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

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

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

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

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

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

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

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

a=40

40+729+2187

d/s:2956

số các số hạng là : (2187 - 1): 2 +1 = 1094

a = (1+2187) x 1094 : 2 = 1196836

3³:9.3ⁿ=729

27:9.3ⁿ=729

3.3ⁿ=729

3ⁿ=729:3

3ⁿ=243

3ⁿ=3⁵

^=>n=5

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.

692157

(2x+1)³=729
=>2x+1=\(\sqrt[3]{729}\)
=>2x+1=9
=>2x=8
=>x=4

tick đúng nha

=> 3^x . 3² = 3⁶

=> 3^x = 3⁴

=> x = 4

3^{x}.3^{x+1}.3^{x+2}>=729`

`=>3^{x+x+1+x+2}>=3^6`

`=>3^{3x+3}>=3^6`

`=>3x+3>=6`

`=>3x>=3=>x>=1`