\(\left(4x-1\right)^2=25.9=225\\ \Leftrightarrow\left(4x-1\right)^2=15^2=\left(-15\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=16\\4x=-14\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{16}{4}=4\\x=-\dfrac{14}{4}=-\dfrac{7}{2}\end{matrix}\right.\)

\(\left(4x-1\right)^2=25\cdot9\)

\(\Rightarrow\left(4x-1\right)^2=5^2\cdot3^2\)

\(\Rightarrow\left(4x-1\right)^2=\left(5\cdot3\right)^2\)

\(\Rightarrow\left(4x-1\right)^2=15^2\)

TH1: \(4x-1=15\)

\(\Rightarrow4x=15+1\)

\(\Rightarrow4x=16\)

\(\Rightarrow x=\dfrac{16}{4}\)

\(\Rightarrow x=4\)

TH2: \(4x-1=-15\)

\(\Rightarrow4x=-15+1\)

\(\Rightarrow4x=-14\)

\(\Rightarrow x=-\dfrac{14}{4}\)

\(\Rightarrow x=-\dfrac{7}{2}\)

846 : [41 - (7x - 5)] = 47

41 - (7x - 5)=846:47=18

7x - 5=41-18=23

7x=23+5=28

x=28:7=4

(4x- 1)² = 25.9

(4x- 1)² =225=15²

4x- 1=15

4x=15+1=16

x=16:4=4

(4x-1)² = 225

(4x-1)² = 15² = (-15)²

<=> 4x-1 = 15 hoặc 4x-1 = -15

4x = 16 hoặc 4x = -14

x = 4 hoặc x = - 3,5

a, b dễ :>>

a) \(2^x=16\)

\(2^x=2^4\)

\(x=4\)

b) \(2^x-15=17\)

\(2^x=17+15\)

\(2^x=32\)

\(2^x=2^5\)

\(x=5\)

Trả lời :

a, 2^x = 16

=> 2^x = 2⁴

=> x = 4

b, 2^x - 15 = 17

=> 2^x = 32

=> 2^x = 2⁵

=> x = 5

c, (4x - 1)² = 25 . 9

=> (4x - 1)² = 225

=> (4x - 1)² = \(\pm\)15²

=> 4x - 1 = \(\pm\)15

\(\Rightarrow\orbr{\begin{cases}4x-1=15\\4x-1=-15\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=4\\x=\frac{-7}{2}\end{cases}}\)

c) \(\left(4x-1\right)^2=25\cdot9\)

\(\left(4x-1\right)^2=225\)

\(\Rightarrow\orbr{\begin{cases}\left(4x-1\right)^2=15^2\\\left(4x-1\right)^2=\left(-15\right)^2\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}4x-1=15\\4x-1=\left(-15\right)\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=4\\x=\frac{-7}{2}\end{cases}}\)

Vậy: ...

[2x +1] ³ =125

[2x +1] ³ =5³

2x +1         =5

2x               =4

x                 =4:2

x                 =2

\(\left(2x+1\right)^3=125\)

\(\left(2x+1\right)^3=5^3\)

\(2x+1=5\)

\(2x=5-1\)

2x=4

x=4/2

x=2

\(\left(4x-1\right)^2=25\cdot9\)

\(\left(4x-1\right)^2=225\)

\(\left(4x-1\right)^2=15^2\)

\(4x-1=15\)

4x=15+1

4x=16

x=16/4

x=4

a: \(x\in\varnothing\)

b: \(\Leftrightarrow\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{7}{2}\end{matrix}\right.\)

a,  x - 3 : 2 = 5 14 : 5 12

=>  x - 3 : 2 = 5 2

=>  x - 3 : 2 = 25

=> x – 3 = 25

=> x = 53

b,  30 : x - 7 = 15 19 : 15 18

=>  30 : x - 7 = 15

=> x – 7 = 2

=> x = 9

c,  x 70 = x

=>  x 70 - x = 0

=>  x ( x 69 - 1 ) = 0

=> 

d,  2 x + 1 3 = 9 . 81

=>  2 x + 1 3 = 9 3

=> 2x + 1 = 9

=> x = 4

e,  5 x + 5 x + 2 = 650

=>  5 x 1 + 5 2 = 650

=>  5 x . 26 = 650

=>  5 x = 25

=> x = 2

f,  4 x - 1 2 = 25 . 9

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

=>  4 x - 1 2 = 15 2

=> 4x – 1 = 15

=> x = 4