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c) 9 < 3^x : 3 < 81

=> 3² < 3^{x - 1} < 3⁴ 

=> x - 1 = {2; 3; 4}

=> x = {3; 4; 5}

d) 5^x . 5^{x + 1} . 5 ^{x + 2} < 2¹⁸ . 5¹⁸ : 2¹⁸ 

=> 5^{x + x + 1 + x + 2} < 2¹⁸ : 2¹⁸ . 5¹⁸ 

=> 5^{3x + 3} < 1.5¹⁸ 

=> 5^{3.(x + 1)} < 5¹⁸ 

=> 3.(x + 1) < 18

=> x + 1 < 18 : 3

=> x + 1 < 6

=> x < 6 - 1

=> x < 5

c. \(9\le3^x:3\le81\)

\(\Rightarrow3^2\le3^{x-1}\le3^4\)

\(\Rightarrow3^{x-1}\in\left\{3^2;3^3;3^4\right\}\)

\(\Rightarrow x-1\in\left\{2;3;4\right\}\)

\(\Rightarrow x\in\left\{3;4;5\right\}\)

d. Thêm đk : x thuộc N

 \(5^x.5^{x+1}.5^{x+2}\le2^{18}.5^{18}:2^{18}\)

\(\Rightarrow5^{x+x+1+x+2}\le5^{18}\)

\(\Rightarrow x+x+x+1+2\le18\)

\(\Rightarrow3x+3\le18\)

\(\Rightarrow3\left(x+1\right)\le18\)

\(\Rightarrow x+1\le6\)

\(\Rightarrow x\le5\)

\(\Rightarrow x\in\left\{1;2;3;4;5\right\}\)

Ta có: \(5^x.5^{x+1}.5^{x+2}\le10^{18}:2^{18}\)

=> \(5^{x+x+1+x+2}\le\left(10:2\right)^{18}\)

=> \(5^{3x+3}\le5^{18}\)

=> 3x+3 < 18

=> 3.(x+1) < 18 

=> x+1 < 18:3

=> x+1 < 6

=> x < 6-1

=> x < 5

Vậy x \(\in\){0; 1; 2; 3; 4; 5}.

5^x*5^x+1*5^x+2<10^18:2^18

5^3x+3<5^18

3x+3<18

3(x+1)<18

x<5

x=1;2;3;4;5.

Bạn nhớ sửa dấu họ mình nhé

5^x.5^(x+1).5^(x+2).2^18<=10^18=2^18.5^18

x+x+1+x+2<=18

3x+3<=18

x+1<=6

x<=5

nếu tự nhiện thì x=(0,1,2,3,4,5)

5^x.5^x+1.5^x+2 = 5¹⁸

⇔5^3x+3 = 5¹⁸

⇔3x+3 = 18

⇔3x = 18-3

⇔3x = 15

⇔x = 5

5^x.5^x+1.5^x+2=5^18

=> 5^3x+1+2=5^18

=> 5^3x+3=5^18

=>3x+3=18

=> x=5

vậy....

ta có : \(5^x.5^{\left(x+1\right)}.5^{\left(x+2\right)}\le\dfrac{100...0}{2^{18}}\) \(\Leftrightarrow5^{3x+3}\le\dfrac{10^{18}}{2^{18}}=5^{18}\)

\(\)\(\Leftrightarrow3x+3\le18\Leftrightarrow x\le5\) vậy \(x\le5\)

cảm ơn nha