1, \(81\cdot27^3\cdot243^5=3^4\cdot3^9\cdot3^{25}=3^{38}\)

2,\(25^4\cdot125^3\cdot625^7=5^8\cdot5^9\cdot5^{28}=5^{45}\)

3,

\(16^3\cdot8^9\cdot64^5\cdot1024=2^{12}\cdot2^{27}\cdot2^{30}\cdot2^{10}=2^{79}\)

Bài 1: Tính bằng 2 cách:

a) 2^5 : 2^4

= 2

b) 3^4 : 3^2

= 3

c) 6^3 : 6^2

= 6

d) 8^4 : 8^2

= 8^2

= 64

e) 7^5 : 7^4

= 7

f) 100^3 : 100

= 100^2

= 10000

Bài 2: Tìm số tự nhiên x, biết:

a) 2^x = 16

2^x = 2^4

x = 4

Vậy x = 4

b) 3^x = 243

3^x = 3^5

x = 5

Vậy x = 5

c) 5^x+1 = 125

5^x + 1 = 5^3

x + 1 = 3

x = 3 - 1

x = 2

Vậy x = 2

\(\left(b\right)3^2+3^4+3^x=3^{10}\)

\(\Rightarrow3^{2+4+x}=3^{10}\Rightarrow2+4+x=10\)

\(\Rightarrow6+x=10\Rightarrow x=10-6=4\)

\(\left(e\right)x.x^2.x^3.x^4=1024\)

\(\Rightarrow x^1.x^2.x^3.x^4=1024\Rightarrow x^{10}=1024\)

Mà \(1024=2^{10}\Rightarrow x=2\)

a,1+2+3+4...+x=45

có số hạng là (x-1)+1

suy ra:x.(x+1):2=45

         x.(x+1)=90

         x.(x+1)=9.10

      suy ra:x=9

        Vậy x=9

2x - 138 = 2³ . 3²

=> 2x - 138 = 72

=> 2x = 72 + 138

=> 2x = 210

=> x = 105

10 + 2x = 4³ . 4²

10 + 2x =1024

2x = 1024 - 10

2x = 1014

x = 507

(3x - 2⁴) . 7³ = 2.7⁴

3x - 2⁴ = 2 . 7⁴ : 7³

3x - 16 = 14

3x = 14 + 16

3x = 30

x = 10

x⁴ = 16

=> x⁴ = 2⁴

=> x = 2

a) \(9< 3^x< 243\)

\(\Leftrightarrow3^2< 3^x< 3^5\)

\(\Rightarrow x\in\left\{3;4\right\}\)

b) Sửa đề: \(3^4.3^x\div9=27\)

\(\Leftrightarrow3^{x+4}=3\)

\(\Rightarrow x+4=1\)

\(\Rightarrow x=-3\)

c) \(3^x\div3^2=243\)

\(\Leftrightarrow3^{x-2}=3^5\)

\(\Rightarrow x-2=5\)

\(\Rightarrow x=7\)

d) \(25< 5^x< 3125\)

\(\Leftrightarrow5^2< 5^x< 5^5\)

\(\Rightarrow x\in\left\{3;4\right\}\)

e) \(2^x-64=2^6\)

\(\Leftrightarrow2^x=64+64=128\)

\(\Leftrightarrow2^x=2^7\)

\(\Rightarrow x=7\)

f) \(2^x\div16=128\)

\(\Leftrightarrow2^x=2^7.2^4\)

\(\Leftrightarrow2^x=2^{11}\)

\(\Rightarrow x=11\)