a) |x-1|-2x=5

\(\Leftrightarrow\) x - 1 - 2x = 5 (đk: x\(\ge\)1 ) (1)

hoặc -x + 1 - 2x = 5 ( đk: x < 1) (2)

(1): \(\Leftrightarrow\) x - 2x = 5 + 1

\(\Leftrightarrow\) - x = 6

\(\Leftrightarrow\) x = -6 (ko thỏa mãn)

(2): \(\Leftrightarrow\) -x + 1 - 2x = 5

\(\Leftrightarrow\) -3x = 4

\(\Leftrightarrow\) x = \(\frac{-4}{3}\) (thỏa mãn)

Vậy: x = \(\frac{-4}{3}\)

b) |9-7x|=5x-3

\(\Leftrightarrow\) 9 - 7x = 5x - 3 (đk: \(\le\) \(\frac{9}{7}\) ) (1)

hoặc -9 + 7x = 5x - 3 (đk: x > \(\frac{9}{7}\) ) (2)

(1): \(\Leftrightarrow\) -7x-5x = -3-9 \(\Leftrightarrow\) -12x = -12 \(\Leftrightarrow\) x = 1 ( thỏa mãn)

(2): \(\Leftrightarrow\) 7x - 5x = -3 + 9 \(\Leftrightarrow\) 2x = 6 \(\Leftrightarrow\) x = 3 ( thỏa mãn)

Vậy: x= 1; 3

c) 5^x+2 = 625

\(\Leftrightarrow\) 5^x . 5² = 5⁴

\(\Leftrightarrow\) 5^x = \(\frac{5^4}{5^2}\)= 5²

^{\(\Leftrightarrow\)} x = 2

d) (2x - 3)² = 36

\(\Leftrightarrow\) \(\left[{}\begin{matrix}2x-3=6\left(đk:x\ge\frac{3}{2}\right)\text{​​}\Leftrightarrow x=4,5\left(TMĐK\right)\\2x-3=-6\left(đk:x< \frac{3}{2}\right)\Leftrightarrow x=-1,5\left(TMĐK\right)\end{matrix}\right.\)

Vậy: x = 4,5; -1,5

(2x-1)⁴=625

=> (2x-1)⁴=5⁴

=> 2x-1=5

=> 2x=5+1

=> 2x=6

=> x=6:2

=> x=3

3^2x+1.11=2673

=> 3^2x+1=2673:11

=> 3^2x+1=243

=> 3^2x+1=3⁵

=> 2x+1=5

=> 2x=5-1

=> 2x=4

=> x=4:2

=> x=2

(2x -1) mũ 4 =625

(2x -1 ) mũ 4 = 5 mũ 4

=> 2x - 1 = 5 hoặc 2x - 1 = -5

=> 2x = 5 + 1 hoặc -5 +1

=>2x =6 hoặc 2x =-4

=> x = 6:2 hoặc x = -4:2

=>x = 3 hoặc x = 2

(2x + 1)² = 625

2x + 1 = 25 hoặc 2x + 1 = -25

*) 2x + 1 = 25

2x = 25 - 1

2x = 24

x = 24 : 2

x = 12

*) 2x + 1 = -25

2x = -25 - 1

2x = -26

x = -26 : 2

x = -13

Vậy x = -13; x = 12

`(2x+1)^2=625`

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

\(\Rightarrow\left[{}\begin{matrix}2x+1=25\\2x+1=-25\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=24\\2x=-26\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=12\\x=-13\end{matrix}\right.\)

(2x + 1)2 = 625

--> (2x + 1)² = 25²

 TH1: 2x +1        = 25

    --> 2x              = 25 - 1

    --> 2x              = 24

    --> x                = 12

TH2: 2x + 1 = -25

    --> 2x       = -25 - 1

    --> 2x       = -26

    --> x         = -13 

Vậy x thuộc {12; -13}

1) ( 2x + 1 )² = 25

=> ( 2x + 1 )² = 5²

=> 2x + 1 = 5 hoặc 2x + 1 = -5

=> 2x = 4 hoặc 2x = -6

=> x = 2 hoặc x = -3

2) 5^x+2 = 625

=> 5^x+2 = 5⁴

=> x + 2 = 4

=> x = 2

3) ( 2x - 3 )² = 36

=> ( 2x - 3 )² = 6²

=> 2x - 3 = 6 hoặc 2x - 3 = -6

=> 2x = 9 hoặc 2x = -3

=> x = 9/2 hoặc x = -3/2

4) ( 2x - 1 )³ = -8

=> ( 2x - 1 )³ = ( -2 )³

=> 2x - 1 = -2

=> 2x = -1

=> x = -1/2

\(\left(x-\dfrac{2}{15}\right)^3=\dfrac{8}{125}\)

\(\left(x-\dfrac{2}{15}\right)^3=\left(\dfrac{2}{5}\right)^3\)

\(x-\dfrac{2}{15}=\dfrac{2}{5}\)

\(x=\dfrac{2}{5}+\dfrac{2}{15}\)

\(x=\dfrac{8}{15}\)

\(\left(\dfrac{4}{5}\right)^{2x+5}=\dfrac{256}{625}\)

\(\left(\dfrac{4}{5}\right)^{2x+5}=\left(\dfrac{4}{5}\right)^4\)

\(2x+5=4\)

\(2x=-1\)

\(x=-0,5\)

\(\left(x-\dfrac{2}{15}\right)^3=\dfrac{8}{125}\\ \Rightarrow\left(x-\dfrac{2}{15}\right)^3=\left(\dfrac{2}{5}\right)^3\\ \Rightarrow x-\dfrac{2}{15}=\dfrac{2}{5}\\ \Rightarrow x=\dfrac{2}{5}+\dfrac{2}{15}\\ \Rightarrow x=\dfrac{6}{15}+\dfrac{2}{15}\\ \Rightarrow x=\dfrac{8}{15}\\ \left(\dfrac{4}{5}\right)^{2x+5}=\dfrac{256}{625}\\ \Rightarrow\left(\dfrac{4}{5}\right)^{2x+5}=\left(\dfrac{4}{5}\right)^4\\ \Rightarrow2x+5=4\\ \Rightarrow2x=4-5\\ \Rightarrow2x=-1\\ \Rightarrow x=-\dfrac{1}{2}\)

\(a,\left(\dfrac{4}{9}\right)^x=\left(\dfrac{3}{2}\right)^{-5}\\ \Leftrightarrow\left(\dfrac{2}{3}\right)^{2x}=\left(\dfrac{2}{3}\right)^5\\ \Rightarrow x=\dfrac{5}{2}\)

Vậy....