a) \(5\left(x+7\right)-10=2^3\cdot5\)

\(\Rightarrow5\left(x+7\right)-10=40\)

\(\Rightarrow5\left(x+7\right)=40+10\)

\(\Rightarrow x+7=\dfrac{50}{5}\)

\(\Rightarrow x+7=10\)

\(\Rightarrow x=10-7\)

\(\Rightarrow x=3\)

b) \(9x-2\cdot3^2=3^4\)

\(\Rightarrow9x-18=81\)

\(\Rightarrow9x=81+18\)

\(\Rightarrow9x=99\)

\(\Rightarrow x=\dfrac{99}{9}\)

\(\Rightarrow x=11\)

c) \(5^{25}\cdot5^{x-1}=5^{25}\)

\(\Rightarrow5^{x-1}=5^{25}:5^{25}\)

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

\(\Rightarrow5^{x-1}=5^0\)

\(\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

a) 5(�+7)−10=23⋅55(x+7)−10=23⋅5

$\Rightarrow 5\left(x+7\right)-10=40$

$\Rightarrow 5\left(x+7\right)=40+10$

⇒�+7=505⇒x+7=550​

$\Rightarrow x+7=10$

$\Rightarrow x=10-7$

$\Rightarrow x=3$

b) 9�−2⋅32=349x−2⋅32=34

$\Rightarrow 9x-18=81$

$\Rightarrow 9x=81+18$

$\Rightarrow 9x=99$

⇒�=999⇒x=999​

$\Rightarrow x=11$

c) 525⋅5�−1=525525⋅5x−1=525

⇒5�−1=525:525⇒5x−1=525:525

⇒5�−1=1⇒5x−1=1

⇒5�−1=50⇒5x−1=50

$\Rightarrow x-1=0$

$\Rightarrow x=1$

Bài 2: 

a: \(\Leftrightarrow\left(x-5\right)\left(x+5\right)-\left(x+5\right)=0\)

=>(x+5)(x-6)=0

=>x=-5 hoặc x=6

b: \(\Leftrightarrow4x^2-4x+1-4x^2+1=0\)

=>-4x+2=0

hay x=1/2

c: \(\Leftrightarrow\left(x^2+4\right)\left(x^2-1\right)=0\)

=>x=1 hoặc x=-1

5ˣ⁺¹ - 5ˣ = 100 . 25²⁹

5ˣ.(5 - 1) = 100 .(5²)²⁹

5ˣ.4 = 100.5⁵⁸

5ˣ = 100 . 5⁵⁸ : 4

5ˣ = 25 .5⁵⁸

5ˣ = 5².5⁵⁸

5ˣ = 5⁶⁰

x = 60

\(5^{x+1}-5^x=100\cdot25^{29}\\\Rightarrow 5^x\cdot5-5^x=2^2\cdot5^2\cdot(5^2)^{29}\\\Rightarrow 5^x\cdot(5-1)=4\cdot 5^2\cdot5^{58}\\\Rightarrow 4\cdot5^x=4\cdot 5^{60}\\\Rightarrow5^x=5^{60}\\\Rightarrow x=60\\Vậy:x=60\)

\(\left(9^{30}-27^{19}\right):3^{57}+\left(125^9-25^{12}\right):5^{24}\)

\(=\left(3^{60}-3^{57}\right):3^{57}+\left(5^{27}-5^{24}\right):5^{24}\)

\(=3^{57}\left(3^3-1\right):3^{57}+5^{24}\left(5^3-1\right):5^{24}\)

\(=3^3-1+5^3-1\)

\(=27-1+125-1\)

\(=150\)

2 )

\(x^2-25-\left(x+5\right)=0\)

\(\Leftrightarrow\left(x+5\right)\left(x-5\right)-\left(x+5\right)=0\)

\(\Leftrightarrow\left(x+5\right)\left(x-5-1\right)=0\)

\(\Leftrightarrow\left(x+5\right)\left(x-6\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=6\end{matrix}\right.\)

Vậy ...

b )

\(\left(2x-1\right)^2-\left(4x^2-1\right)=0\)

\(\Leftrightarrow4x^2-4x+1-4x^2+1=0\)

\(\Leftrightarrow2-4x=0\)

\(\Leftrightarrow4x=2\)

\(\Leftrightarrow x=\dfrac{1}{2}\)

Vậy ...

c )

\(x^2\left(x^2+4\right)-x^2-4=0\)

\(\Leftrightarrow x^2\left(x^2+4\right)-\left(4+x^2\right)=0\)

\(\Leftrightarrow\left(x^2-1\right)\left(x^2+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-1=0\\x^2+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x^2=1\\x^2=-4\left(L\right)\end{matrix}\right.\)

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

Vậy ...

mk not biết

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

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

\(\Rightarrow x+1=3\)

\(x=2\)

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

\(< =>\left(x+1\right)^3=3.3.3=3^3\)

\(< =>x+1=3< =>x=3-1=2\)

\(\left(2x+3\right)^3=9.81\)

\(< =>\left(2x+3\right)^3=9.9.9\)

\(< =>\left(2x+3\right)^3=9^3\)

\(< =>2x+3=9< =>2x=6\)

\(< =>x=\frac{6}{2}=3\)

giúp mình bài này đi

21.73 + 27 . 21

a) 5^x = 125

5^x = 5³

=> x = 3

b) x³ = 64

x³ = 4³

=> x = 4

c) ( x - 1 ) ² = 25

( x - 1 ) ² = 5²

=> x - 1 = 5

=> x = 5 + 1

=> x = 6

d) 5^x + 5^x+2 = 130

5^x . 1 + 5^x . 5² = 130

5^x . ( 1 + 5² ) = 130

5^x . 26 = 130

5^x = 130 : 26

5^x = 5

=> x = 1

\(a.\)\(5^x=125\)

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

\(b.\)\(x^3=64\)

\(x^3=4^3\Rightarrow x=4\)

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

\(x^2=5^2\)mà \(\left(x-1\right)\)nên \(x=5+1=6\)

P/s: Ý d thiếu nhé bạn 

a)5^x=125

5^x=5³

=>x=3

b)tương tụ câu a

c)(x-1)²=25

(x-1)²=5²

=>x-1=5

x=5+1

x=6

d)thiếu đề!

  Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)

Bài 3

2\(^x\) = 16

2\(^x\) = 2⁴

  \(x=4\)

Vậy \(x=4\)

a)  4^x = 64

     4^x =  4³

=> x = 3

c)   5^x+2 = 25

      5^x+2 = 5²

=> x + 2 = 2

=>        x = 0

mình thấy phần b hình như sai đề

Có:

a)\(4^x=64=4^3=>x=3\)

b)\(2^{x+1}=25=>2^x.2=25\Rightarrow2^x=25:2=12,5\)

=> ....

c)\(5^{x+2}=25\Rightarrow5^x.5^2=25=>5^x.25=25=>5^x=25:25=1\)

=>x=0

a) 

\(4^x=64\)

Ta thấy \(64=4^3\Rightarrow x=3\)

c) 

\(5^{x+2}=25\)

Ta thấy : \(25=5^2\)

Nếu \(x=1\)thì \(5^3=125\)(loại)

Nếu \(x=0\)thì \(5^{0+2}=5^2=25\)(chọn)

=> x = 0 

P/S : Phần b vừa thiếu vừa sai đề 

3^4 . 9 .3^x = 3^7

3^4 . 3^2 . 3^x = 3^7

3^6 . 3^x = 3^7

3^x = 3

x = 1

4^x . 4^1 = 16

4^x = 16 : 4

 4^x =4

=> x=1

5^x : 5 = 25

5^x = 25 . 5 =125

=> x = 3