a) 

5²x .5  = 3125

25x .5 = 3125

25x     = 3125 : 5

25x     = 625

x         = 625 : 25

x         = 25

a) 5^2x . 5 = 3125

5^{2x + 1} = 5⁵

\(\Rightarrow\)2x + 1 = 5

\(\Rightarrow\)2x = 5 - 1 = 4

\(\Rightarrow\)x = 4 : 2 = 2

b) 5^x + 5^{x + 3} = 630

5^x + 5^x . 5³ = 630

5^x . ( 1 + 5³ ) = 630

5^x . 126 = 630

5^x = 630 : 126

5^x = 5

\(\Rightarrow\)x = 5

c) 3^{2x + 1} = 243

3^{2x + 1} = 3⁵

\(\Rightarrow\)2x + 1 = 5

\(\Rightarrow\)2x = 5 - 1 = 4

\(\Rightarrow\)x = 4 : 2 = 2

d) 3^{2x + 1} = 9

3^{2x + 1} = 3²

\(\Rightarrow\)2x + 1 = 2

\(\Rightarrow\)2x = 2 - 1 = 1

\(\Rightarrow\)x = 1 : 2 = \(\frac{1}{2}\)

a) 5^2x.5=3135

=> 5^2x   =3125:5

=> 5^2x   =625

=> 5^2x   = 5^4

=> 2x       =4

=>   x       =4:2

=>  x        =2

Vậy x=2

_

chị chỉ gợi ý cko em cách làm được không ?

3^ x . 3^ 2= 729

3^ x  . 9        = 729

3^ x               = 729: 9

3^x                 =81 

vậy    x            = 3^3

5^ x . 625 = 3125

5^x           = 3125:625

5^x            =   5

vậy x          = 1

( 2x+1 )^ 3 = 27

( 2x+1) ^ 3 = 3^3

vậy 2x+1 =  3

  vậy x = 0         

3906/3125

`@` `\text {Ans}`

`\downarrow`

`9^8 \div 3^2`

`= (3^2)^8 \div 3^2`

`= 3^16 \div 3^2`

`=`\(3^{16-2}=3^{14}\)

_____

`3^7 * 27^5 * 81^3`

`= 3^7*(3^3)^5 * (3^4)^3`

`= 3^7 * 3^15 * 3^12`

`=`\(3^{7+15+12}\)

`= 3^34`

______

`36^5 \div 18^5`

`= (36 \div 18)^5`

`= 2^5 = 32`

______

`24*5^5 + 5^2*5^3`

`= 24*5^5 + 5^5`

`= 5^5*(24+1)`

`= 5^5 * 25`

`= 5^5*5^2`

`= 5^7`

______

`125^4 \div 5^8`

`= (5^3)^4 \div 5^8`

`= 5^12 \div 5^8`

`= 5^4`

_____

`@` Phép nâng lên lũy thừa: \(\left(a^m\right)^n=a^{m\cdot n}\) 

`@` Chia lũy thừa cùng cơ số: \(a^m\div a^n=a^{m-n}\)

`@` Nhân lũy thừa cùng cơ số: \(a^m\cdot a^n=a^{m+n}\)

\(9^8:3^2\)

\(=\left(3^2\right)^8:3^2\)

\(=3^{16}:3^2\)

\(=3^{14}\)

=============

\(3^7\cdot27^5\cdot81^3\)

\(=3^7\cdot\left(3^3\right)^5\cdot\left(3^4\right)^3\)

\(=3^7\cdot3^{15}\cdot3^{12}\)

\(=3^{7+12+15}\)

\(=3^{34}\)

===============

\(36^5:18^5\)

\(=\left(36:18\right)^5\)

\(=2^5\)

\(=32\)

=============

\(24\cdot5^5+5^2\cdot5^3\)

\(=24\cdot5^5+5^5\)

\(=5^5\cdot\left(24+1\right)\)

\(=5^5\cdot25\)

\(=5^5\cdot5^2\)

\(=5^7\)

==============

\(125^4:5^8\)

\(=\left(5^3\right)^4:5^8\)

\(=5^{12}:5^8\)

\(=5^4\)

Bài 1:

a) \(\dfrac{10^6\times10^2}{1000^3}=\dfrac{10^{6+2}}{\left(10^3\right)^3}=\dfrac{10^8}{10^9}=\dfrac{1}{10}\)

b)\(\dfrac{625^2\times57\times3125}{25}=\dfrac{\left(5^4\right)^2\times5^5\times57}{5^2}=\dfrac{5^{13}\times57}{5^2}=5^{11}\times57\)

Bài 2 :

a) (x - 5)⁵ = (x - 5)¹⁰

⇒ x - 5 = 0 hoặc x - 5 = 1

⇒ x ∈ {5 ; 6}

\(5^x.5^{x+1}.5^{x+2}=3125\)

\(\Rightarrow5^{x+x+1+x+2}=5^5\)

\(\Rightarrow5^{3x+3}=5^5\)

\(\Rightarrow3x+3=5\)

\(\Rightarrow3x=2\)

\(\Rightarrow x=\frac{2}{3}\)

=> 5^x.5^x+1.5^x+2 = 5⁵

<=> 5^x+x+1+x+2 = 5⁵

=> x+x+1+x+2 = 5

=> 3x+3=5

3x = 5-3

3x = 2

x = 2:3

x = 2/3

5^x . 5^x+1.5^x+2=3125

5^x . 5^x .5¹ + 5^x .5²=3125

5^x  . ( 5¹ + 5² ) = 3125

5^x . 30 = 3125

5^x = 3125 : 30

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