x^28=x

Vậy x=0

(x+1)^5=32

32=2^5

suy ra (x+1)=2

Vậy x=1

x²⁸ = x

+ Với x = 0, ta có: 0²⁸ = 0, đúng

+ Với x khác 0; ta có: x²⁸ = x

Giản ước cả 2 vế đi x ta được x²⁷ = 1 = 1²⁷

=> x = 1

Vậy x thuộc {0 ; 1}

(x + 1)⁵ = 32

=> (x + 1)⁵ = 2⁵

=> x + 1 = 2

=> x = 2 - 1

=> x = 1

Vậy x = 1

(2x + 3)⁵ = 243

=> (2x + 3)⁵ = 3⁵

=> 2x + 3 = 3

=> 2x = 3 - 3

=> 2x = 0

=> x = 0 : 2

=> x = 0

Vậy x = 0

Ủng hộ mk nha ^_-

a) Ta có :  2 x : 2 2 = 2 5  nên x = 7.

b) Ta có:  3 x : 3 2 = 3 5  nên x = 7.

c) Ta có :  4 4 : 4 x = 4 2  nên x = 2.

d) Ta có :  5 x : 5 2 = 5 2  nên x = 4,

e) Ta có:  5 x + 1 : 5 = 5 4  nên x = 4.

f) Ta có :  4 2 x - 1 : 4 = 4 2  nên x = 2

2/3^2x-1=3/243

2/3^2x-1=(2/3)^5

suy ra 2x-1=5

            2x =5+1

            2x =6

              x = 6:2

               x = 3

     vay x=3

\(a,3^x>\dfrac{1}{243}\\ \Leftrightarrow3^x>3^{-5}\\ \Leftrightarrow x>-5\\ b,\left(\dfrac{2}{3}\right)^{3x-7}\le\dfrac{3}{2}\\ \Leftrightarrow3x-7\le1\\ \Leftrightarrow3x\le8\\ \Leftrightarrow x\le\dfrac{8}{3}\\ c,4^{x+3}\ge32^x\\ \Leftrightarrow2^{2x+6}\ge2^{5x}\\ \Leftrightarrow2x+6\ge5x\\ \Leftrightarrow3x\le6\\ \Leftrightarrow x\le2\)

d, Điều kiện: x > 1

\(log\left(x-1\right)< 0\\ \Leftrightarrow x-1< 1\\ \Leftrightarrow1< x< 2\)

e, Điều kiện: \(x>\dfrac{1}{2}\)

\(log_{\dfrac{1}{5}}\left(2x-1\right)\ge log_{\dfrac{1}{5}}\left(x+3\right)\\ \Leftrightarrow2x-1\ge x+3\\ \Leftrightarrow x\ge4\)

f, Điều kiện: x > 4

\(ln\left(x+3\right)\ge ln\left(2x-8\right)\\ \Leftrightarrow x+3\ge2x-8\\\Leftrightarrow4< x\le11\)

a)

\(3^{2x}=243=3^5\)

=> 2x = 5

=> x = 5/2

b)

\(4^{x+1}=\left(2^2\right)^{x+1}=2^{2x+2}\)

\(\Rightarrow2^{2x+2}=32=2^5\)

=> 2x + 2 = 5

=> 2x = 3

=> x = 3/2

\(a,3^{2x}=243\Leftrightarrow2x=5\)

\(\Rightarrow x=5:2=2,5.\)

Vậy \(x=2,5.\)

\(b,4^{x+1}=32\Leftrightarrow2^{2x+2}=32\)

\(\Rightarrow2x+2=5\)

\(\Rightarrow x=1,5.\)

Vậy \(x=1,5.\)

\(a)\)\(\left(\frac{3}{5}\right)^{2x+1}=\frac{81}{625}\)

\(\Leftrightarrow\)\(\left(\frac{3}{5}\right)^{2x+1}=\left(\frac{3}{5}\right)^4\)

\(\Leftrightarrow\)\(2x+1=4\)

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

Vậy \(x=\frac{3}{2}\)

\(b)\)\(\left(\frac{2}{3}\right)^x.\left(\frac{2}{3}\right)^3=\frac{32}{243}\)

\(\Leftrightarrow\)\(\left(\frac{2}{3}\right)^{x+3}=\left(\frac{2}{3}\right)^5\)

\(\Leftrightarrow\)\(x+3=5\)

\(\Leftrightarrow\)\(x=2\)

Vậy \(x=2\)

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

\(\Leftrightarrow\)\(\left(2x-1\right)^3-\left(2x-1\right)^2=0\)

\(\Leftrightarrow\)\(\left(2x-1\right)^2\left(2x-1-1\right)=0\)

\(\Leftrightarrow\)\(\left(2x-1\right)^2\left(2x-2\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}\left(2x-1\right)^2=0\\2x-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=1\end{cases}}}\)

Vậy \(x=\frac{1}{2}\) hoặc \(x=1\)

Chúc bạn học tốt ~ 

\(\Leftrightarrow\left(3:\dfrac{4}{32}\cdot x-1\right)^5=243\)

\(\Leftrightarrow\left(24x-1\right)^5=243\)

=>24x-1=3

=>24x=4

hay x=1/6