\(5^{2x-3}-2.5^2=5^2.3\)

\(\Rightarrow5^{2x-3}=5^2.3+5^2.2\)

\(\Rightarrow5^{2x-3}=5^2.\left(2+3\right)=5^3\)

\(\Rightarrow2x-3=3\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=3\)

\(5^{2x-3}\)-2.\(5^2\)= \(5^2\).3

\(5^{2x-3}\) _2.25=25.3

\(5^{2x-3_{ }}\)_50=75

\(5^{2x-3}\)= 75_50

\(5^{2x-3}\)= \(5^2\)

suy ra : 2x-3=2

2x=2.3

2x=6

x=6:2

x=3

1. 

$(3^2-2^3)x+3^2.2^2=4^2.3$

$\Leftrightarrow x+36=48$

$\Leftrightarrow x=48-36=12$

2.

$x^5-x^3=0$

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

$\Leftrightarrow x^3(x-1)(x+1)=0$

$\Leftrightarrow x^3=0$ hoặc $x-1=0$ hoặc $x+1=0$

$\Leftrightarrow x=0$ hoặc $x=\pm 1$
3.

$(x-1)^2+(-3)^2=5^2(-1)^{100}$

$\Leftrightarrow (x-1)^2+9=25$

$\Leftrightarrow (x-1)^2=25-9=16=4^2=(-4)^2$

$\Rightarrow x-1=4$ hoặc $x-1=-4$

$\Leftrightarrow x=5$ hoặc $x=-3$

4.

$(2x-1)^2-(2x-1)=0$

$\Leftrightarrow (2x-1)(2x-1-1)=0$

$\Leftrightarrow (2x-1)(2x-2)=0$

$\Leftrightarrow 2x-1=0$ hoặc $2x-2=0$

$\Leftrightarrow x=\frac{1}{2}$ hoặc $x=1$

$\Lef

`@` `\text {Ans}`

`\downarrow`

\((3^2-2^3)x+3^2.2^2=4^2.3\)

`=> x + (3*2)^2 = 48`

`=> x+6^2 = 48`

`=> x + 36 = 48`

`=> x = 48 - 36`

`=> x=12`

Vậy, `x=12`

\(x^5-x^3=0\)

`=> x^3(x^2 - 1)=0`

`=>`\(\left[{}\begin{matrix}x^3=0\\x^2-1=0\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=0\\x^2=1\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=0\\x=\pm1\end{matrix}\right.\)

Vậy, `x \in {0; +- 1 }`

\(\left(x-1\right)^2+\left(-3\right)^2=5^2\cdot\left(-1\right)^{100}\)

`=> (x-1)^2 + 9 = 25*1`

`=> (x-1)^2 + 9 = 25`

`=> (x-1)^2 = 25 - 9`

`=> (x-1)^2 = 16`

`=> (x-1)^2 = (+-4)^2`

`=>`\(\left[{}\begin{matrix}x-1=4\\x-1=-4\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=4+1\\x=-4+1\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\)

Vậy, `x \in {5; -3}`

\((2x-1)^2-(2x-1)=0\)

`=> (2x-1)(2x-1) - (2x-1)=0`

`=> (2x-1)(2x-1-1)=0`

`=>`\(\left[{}\begin{matrix}2x-1=0\\2x-2=0\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}2x=1\\2x=2\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\end{matrix}\right.\)

Vậy, `x \in {1; 1/2}`

e) 96-5(2x-1)=41

5(2x-1)= 96-41

5(2x-1)=55

2x-1=55:5

2x-1=11

2x=11+1

2x=12

x=12:2

x=6

b) x + 2/5 = 2-3x/3

x + 2/5 = 2 -x

x +x = 2 - 2/5

2x= 8/5

x = 8/5 x 1/2

x = 4/5

c) 2. 3^x . 3^2 = 18

3^x+2 = 18:2

3^ x+2 = 9

3^ x+2 = 3^2

=> x+2 = 2

=> x=0

a) TH1: 2x-1 = x + 2

2x-x = 2+1

x =3

TH2 : 2x-1 = -(x+2)

2x-1 = -x-2

2x +x = -2 +1

3x = -1

x = -1/3

mk chi lam duoc cau c thoi

suy ra 2x-1=5 hoac 2x-1=-5

          2x=6            2x=-4

          x=3                 x=-2

vay x=3 hoac x=-2

a. 3/4.x+1/3=-1/2

=>3/4.x=-1/2-1/3=-5/6

=>x=-5/6 chia 3/4=-10/9

b. -x/4=-9/x =>-x*x=4*-9

=>-2x=-36 =>x=18

c./2x-1/=5

=> 2x-1=5 =>2x=5+1=6 =>x=3

  hoặc 2x-1=-5 =>2x=-5+1=-4 =>x=-2

d,e: Sai đề rồi

a, 7\(x\) - \(x\) = 5²¹ : 5¹⁹ + 3.2².7

     6\(x\)    = 5³ + 3.4.7

    6\(x\)    = 125 + 12.7

    6\(x\)  = 125 + 84

    6\(x\) = 209

     \(x\)  = 209 : 6

    \(x\) = \(\dfrac{209}{6}\)

b; 11\(x\) - 7\(x\) + 3⁴ : 3³ = 5⁴ + 2\(x\)

    4\(x\) + 3 = 625 + 2\(x\)

   4\(x\) - 2\(x\) = 625 - 3

   2\(x\)        = 622

     \(x\)        = 622 : 2

    \(x\)        = 311

c; 75 - 5.(\(x-3\))³ = 700

          5.(\(x\) - 3)³ = 700 - 75

         5.(\(x\) - 3)³ = - 625

           (\(x\) - 30)³ = - 625 : 5

           (\(x\) - 30)³ = - 125

           (\(x-3\))³ =  (-5)³

           \(x\) - 3 = - 5 

           \(x\)         = - 5 + 3

            \(x\)       = -2

d, 3.(2\(x\) - 1)² = 75

       (2\(x\) - 1)² = 75 : 3

       (2\(x\) - 1)² = 25

       \(\left[{}\begin{matrix}2x-1=-5\\2x-1=5\end{matrix}\right.\)

       \(\left[{}\begin{matrix}2x=-5+1\\2x=5+1\end{matrix}\right.\)

       \(\left[{}\begin{matrix}2x=-4\\2x=6\end{matrix}\right.\)

       \(\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)

d) \(3.\left(2x-1\right)^2=75\)

\(\left(2x-1\right)^2=75\div3\)

\(\left(2x-1\right)^2=25\)

\(\left(2x-1\right)^2=5^2\) 

\(\Rightarrow2x-1=5\) 

\(2x=5+1\)               

\(2x=6\)                     

\(x=6\div2\)                  

\(x=3\)