\(26\cdot5^{x-1}-5^{x-1}=125\)

\(\Rightarrow5^{^{x-1}}\cdot\left(26-1\right)=125\)

\(\Rightarrow5^{x-1}\cdot25=125\)

\(\Rightarrow5^{x-1}=\dfrac{125}{25}\)

\(\Rightarrow5^{x-1}=5\)

\(\Rightarrow x-1=1\)

\(\Rightarrow x=1+1\)

\(\Rightarrow x=2\)

\(\Leftrightarrow5^{x-1}\cdot\left(26-1\right)=125\)

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

=>x-1=1

=>x=2

(5^2.x-5^x+1)/5=125

25.x-5^x+1=625

\(a,4^{2x-6}=1\)\(\Leftrightarrow2x-6=0\Leftrightarrow2x=6\Rightarrow x=3\)

\(b,2^{2x-1}=16\Rightarrow2^{2x-1}=2^4\)

\(\Rightarrow2x-1=4\Rightarrow2x=5\Rightarrow x=\frac{5}{2}\)

\(c,5< 5^x< 125\Rightarrow5^1< 5^x< 5^3\)\(\Rightarrow1< x< 3\)

\(d,5^{x+1}=125\Rightarrow5^{x+1}=5^3\Rightarrow x+1=3\Rightarrow x=2\)

\(a,4^{2x-6}=1\)

\(4^{2x-6}=4^0\)

\(\Rightarrow2x-6=0\)

\(\Rightarrow2x=6\Leftrightarrow x=3\)

\(b,2^{x-1}=16\)

\(2^{x-1}=2^4\)

\(\Rightarrow x-1=4\)

\(\Rightarrow x=5\)

`@` `\text {Ans}`

`\downarrow`

`a)`

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

`=> 5*x^3 = 0+5`

`=> 5*x^3 = 5`

`=> x^3 = 5 \div 5`

`=> x^3 = 1`

`=> x^3 = 1^3`

`=> x=1`

Vậy, `x=1.`

`b)`

\(( x+1)^2 = 16\)

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

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

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

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

Vậy, `x \in {3; -5}`

`c)`

\(( x+1)^3 = 27\)

`=> (x+1)^3 = 3^3`

`=> x+1=3`

`=> x=3-1`

`=> x=2`

Vậy, `x=2.`

`d)`

\(( x-1)^3 = 343\)

`=> (x-1)^3 = 7^3`

`=> x-1=7`

`=> x=7+1`

`=> x=8`

Vậy, `x=8.`

`e)`

\((2x - 1^3) = 125\) hay đề là `(2x-1)^3 = 125` vậy ạ?

Mình làm cả 2 TH nhé!

`(2x-1^3)=125`

`=> 2x-1=125`

`=> 2x=125+1`

`=> 2x=126`

`=> x=126 \div 2`

`=> x=63`

TH2:

`(2x-1)^3 = 125`

`=> (2x-1)^3 = 5^3`

`=> 2x-1=5`

`=> 2x=5+1`

`=> 2x=6`

`=> x=6 \div 2`

`=> x=3`

Vậy, `x=3.`

(a) \(5x^3-5=0\Leftrightarrow5x^3=5\Leftrightarrow x^3=1\Leftrightarrow x=1\)

(b) \(\left(x+1\right)^2=16\Rightarrow\left[{}\begin{matrix}x+1=4\\x+1=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)

(c) \(\left(x+1\right)^3=27\Leftrightarrow x+1=3\Leftrightarrow x=2\)

(d) \(\left(x-1\right)^3=343\Leftrightarrow x-1=7\Leftrightarrow x=8\)

(e) \(\left(2x-1\right)^3=125\Leftrightarrow2x-1=5\Leftrightarrow2x=6\Leftrightarrow x=3\)

3^x=234—> 243 chứ bạn

3^x=243

Vì 3⁵=243

Nên x=5

3^x=4096

6^x=216

Vì 6³=216

Nên x=3

5.3^x=405

3^x=405:5

3^x=81

Vì 3⁴=81

Nên x=4

2^x=4

Vì 2²=4

Nên x=2

x⁵=32

Vì 2⁵=32

Nên x=5

x⁴=81

Vì 3⁴=81 và (-3)⁴=81

Nên x=3 hoặc x=-3

(x—2)⁵=243

(x—2)⁵=3⁵

Nên x—2=3

x=3+2

x=5

(x—1)⁴=16

(x—1)⁴=2⁴  

Nên x—1 =2 hoặc x—1=-2

x=2+1 hoặc x=-2 +1

x=3 hoặc x=-1

(x+1)³=125

(x+1)³=5³

Nên x+1=3

x=3-1

x=1

(x—2)³=64

(x—2)³=4³

Nên x—2=4

x=4+2

x=6

(x—1)⁵=32

(x—1)⁵=2⁵

==> x—1=5

x=5+1

x=6

\(3^x=243\Rightarrow3^x=3^5\Rightarrow x=5\)

câu thứ 2 mn chịu

\(6^x=216\Rightarrow6^x=6^3\Rightarrow x=3\)

\(5.3^x=405\\ 3^x=405:5\\ 3^x=81\\ \Rightarrow3^x=3^4\\ \Rightarrow x=4\)

\(2^x=4\\ \Rightarrow2^x=2^2\\ \Rightarrow x=2\)

\(x^5=32\\ \Rightarrow x^5=2^5\\ \Rightarrow x=2\)

câu 7 mn ko hỉu

\(x^4=81\\ x^4=\left(+-3\right)^4\\ x=+-3\)

câu 9 mn chịu 

5^x+1=125

5^x+1=5³

=>x+1=3

=>x=2

hình như bạn sai đề rồi thì phải

Tìm x : (5^2x . 5^x+1) :5 = 125

=> 5^x ( 5² . 5¹ ) = 625

=> 5^x . 125    = 625 

=> 5^x           =  5 

=> x = 1 

Study well 

Ai giải hộ e với e phải đi học

a. 8 + (x - 9) = 125 - 64

8 + (x - 9) = 61

x - 9 = 53

x = 62

b. 5 x (X + 7) - 10 = 8 x 5

5 x (X + 7) - 10 = 40

5 x (X + 7) = 50

X + 7 = 10

X = 3