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

g.\(3^{x-1}\)=\(\frac{1}{243}\)

\(3^{x-1}\)=\(\frac{1}{3^5}\)

\(3^{x-1}\)=\(3^{-5}\)

x-1=-5

x=-4

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

\(3^{2x+1}=243\)

\(\Rightarrow3^{2x+1}=3^5\)

\(\Rightarrow2x+1=5\)

\(\Rightarrow2x=5-1\)

\(\Rightarrow2x=4\)

\(\Rightarrow x=4:2\)

\(\Rightarrow x=2\)

\(3^2x+1=243\)

\(9x=243-1\)

\(9x=242\)

\(x=242:9\)

\(\Rightarrow x=\dfrac{242}{9}\)

\(a.\) \(\left(x-2\right)^3:3=-9\)

\(\Leftrightarrow\left(x-2\right)^3=-9.3\)

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

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

\(\Leftrightarrow x-2=-3\)

\(\Leftrightarrow x=-3+2\)

\(\Leftrightarrow x=-1\)

\(b.\) \(3^{x-1}=\frac{1}{243}\)

\(\Leftrightarrow3^x:3=\frac{1}{243}\)

\(\Leftrightarrow3^x=\frac{1}{243}.3\)

\(\Leftrightarrow3^x=\frac{1}{81}\)

\(\Leftrightarrow3^x=3^{-4}\)

\(\Leftrightarrow x=-4\)

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

\(\Leftrightarrow\orbr{\begin{cases}\left(2x-3\right)^2=\frac{1}{2}^2\\\left(2x-3\right)^2=\left(-\frac{1}{2}\right)^2\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-3=\frac{1}{2}\\2x-3=-\frac{1}{2}\end{cases}}\)

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

\(\Leftrightarrow\orbr{\begin{cases}2x=\frac{7}{2}\\2x=\frac{5}{2}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{2}:2=\frac{7}{4}\\x=\frac{5}{2}:2=\frac{5}{4}\end{cases}}\)

\(d.\) Thiếu đề rồi bn !!!

Câu d bn vt nhầm đề đúng ko ???

\(d.\) \(2^x+2^{x-3}=144\)

\(\Leftrightarrow2^x.1+2^x:2^3=144\)

\(\Leftrightarrow2^x.1+2^x.\frac{1}{8}=144\)

\(\Leftrightarrow2^x.\left(1+\frac{1}{8}\right)=144\)

\(\Leftrightarrow2^x.\frac{9}{8}=144\)

\(\Leftrightarrow2^x=144:\frac{9}{8}\)

\(\Leftrightarrow2^x=128\)

\(\Leftrightarrow2^x=2^7\)

\(\Leftrightarrow x=7\)

a.\(3^{x-1}=243\)

\(3^x:3^1=243\)

\(3^x=729\)

\(\Leftrightarrow3^6=729\)

\(\Leftrightarrow x=6\)

b.\(\left(\dfrac{2}{3}\right)^{x+1}=\dfrac{8}{4}\)

\(\left(\dfrac{2}{3}\right)^x.\left(\dfrac{2}{3}\right)=\dfrac{8}{4}\)

\(\left(\dfrac{2}{3}\right)^x=3\)

Câu b tính đến đây rồi không mò đc x nữa.