3^ x -1 = 1/243

3^x =1/243 +1

3^x = 244 / 243

Ta  thấy đây ko phải lũy thừa của 3 => Ko có x thỏa mãn

81^-2x . 27^x =9^5

81^-2 . 81^x . 27^x =9^5

1/9^4 . (81.27)^x =9 ^5

            3^6x = 9^5 : 1/9^4

             3^6x = 9^9

            3^6x = 3^18

    => 6x =18

  x=3

2^x +2^x +3 =144

2.(2^x) =141

2^x+1 = 141

Ta thấy 141 ko phải lũy thừa của 2 => ko có x thỏa mãn

a. (x - 2)² = 1

<=> (x - 2)² = 1² = (-1)²

<=> \(\begin{cases}x-2=1\\x-2=-1\end{cases}\Leftrightarrow\begin{cases}x=3\\x=1\end{cases}\)

Vậy x \(\in\){1; 3}.

b. (2x - 1)³ = -8

<=> (2x - 1)³ = (-2)³

<=> 2x - 1 = -2

<=> 2x = -2 + 1

<=> 2x = -1

<=> x = -1/2

Vậy x = -1/2.

c. (x + 1/2)² = 1/16

<=> (x + 1/2)² = (1/4)² = (-1/4)²

<=> \(\begin{cases}x+\frac{1}{2}=\frac{1}{4}\\x+\frac{1}{2}=-\frac{1}{4}\end{cases}\Leftrightarrow\begin{cases}x=-\frac{1}{4}\\x=-\frac{3}{4}\end{cases}\)

Vậy x \(\in\){-1/4; -3/4}.

d. (x - 2)³ = -27

<=> (x - 2)³ = (-3)³

<=> x - 2 = -3

<=> x = -3 + 2

<=> x = -1

Vậy x = -1.

a.\(\left(x-2\right)^2\)=1

<=> x-2=1 hoặc x-2=-1

<=> x= 3 hoặc x=1

b.\(\left(2x-1\right)^3\)=-8

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

2x-1=-2

2x=-1

x=-1/2

c.\(\left(x+\frac{1}{2}\right)^2\)=\(\frac{1}{16}\)

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

x+\(\frac{1}{2}\)=\(\frac{1}{4}\)  hoặc x+\(\frac{1}{2}\)=-\(\frac{1}{4}\)

x=-\(\frac{1}{4}\)hoặc x=-\(\frac{3}{4}\)

d.\(\left(x-2\right)^3\)=-27

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

x-2=-3

x=-1

a) \(81^{-2x}.27^x=9^5\)

\(\Rightarrow\left(3^4\right)^{-2x}.\left(3^3\right)^x=3^{10}\)

\(\Rightarrow3^{-8x}.3^{3x}=3^{10}\)

\(\Rightarrow3^{-5}=3^{10}\)

\(\Rightarrow-5x=10\)

\(\Rightarrow x=-2\)

Vậy \(x=-2\)

b) \(2^x+2^{x+3}=144\)

\(\Rightarrow\left(1+2^3\right).2^x=144\)

\(\Rightarrow\left(1+8\right).2^x=144\)

\(\Rightarrow9.2^x=144\)

\(\Rightarrow2^x=16\)

\(\Rightarrow x=4\)

Vậy \(x=4\)

c) \(2^{x-1}+5.2^{x-2}=7.32\)

\(\Rightarrow\left(2+5\right).2^{x-2}=244\)

\(\Rightarrow7.2^{x-2}=244\)

\(\Rightarrow2^{x-2}=32\)

\(\Rightarrow x-2=5\)

\(\Rightarrow x=7\)

Vậy \(x=7\)

a) (X - 2)\(^2\) = 1 <=> X - 2 = \(\sqrt{1}\) <=> X = 1 + 2 <=> X = 3

a) \(\left(2x+3\right)^2=\frac{9}{144}\)

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

\(\Rightarrow\orbr{\begin{cases}2x+3=\frac{1}{4}\\2x+3=\frac{-1}{4}\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=\frac{-11}{4}\\2x=\frac{-13}{4}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{-11}{8}\\x=\frac{-13}{8}\end{cases}}}\)

Vậy ...

b) Ta có: \(\left(3x-1\right)^3=\frac{-8}{27}=\left(\frac{-2}{3}\right)^3\)

\(\Leftrightarrow3x-1=\frac{-2}{3}\Leftrightarrow3x=\frac{1}{3}\Leftrightarrow x=\frac{1}{9}\)

Vậy ....

c) \(x^{10}=25x^8\Leftrightarrow x^{10}:x^8=25\Leftrightarrow x^2=25\Leftrightarrow x=\left\{5;-5\right\}\)

Vậy ...

d) \(\frac{x^7}{81}=27\Leftrightarrow x^7=27.81=2187\)

Mà 3⁷ = 2187 => x⁷ = 3⁷ => x = 3

Vậy ....

e) \(\frac{x^8}{9}=729\Leftrightarrow x^8=729.9=6561\)

Mà 3⁸ = (-3)⁸ = 6561

=> x⁸ = 3⁸ = (-3)⁸

=> x = {-3;3}

Vậy ...

1/vì (1,78^2x-2-1,78^x):1,78^x=0

nên 1,78^x2-2-1,78^x=0     

=>1,78^2x-2=1,78^x

^=>2x-2=x

^2x=x+2

^=>x=2

2/vì cơ số bằng nhau nên ta có

x-2=1;-1;0

ta có:    x-2=1 =>  x=3

            x-2=-1 => x=1

             x-2=0 => x=2

3/ta có

(x+2)³=3³  =>x+2=3    =>x=1

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