a).

\(2.16=2.2^4=2^5\\ 4=2^2\)

theo đề bài, ta có: \(2^5\ge2^n>2^2\Rightarrow5\ge n>2\)

vì n là số tự nhiên nên : \(n=5;4;3\)

b).

\(9.27=3^2.3^3=3^5\\ 243=3^5\)

theo đề bài, ta có: \(3^5\le3^n\le3^5\Rightarrow5\le n\le5\)

=> n=5

Giải:

a)2.16\(\ge\)2ⁿ>4

2.2⁴\(\ge\)2ⁿ>2²

2⁵\(\ge\)2ⁿ>2²

\(\Rightarrow\)5\(\ge\)n>2

\(\Rightarrow\)n\(\in\){3;4;5}

b)9.27\(\le\)3ⁿ\(\le\)243

3².3³\(\le\)3ⁿ\(\le\)3⁵

3⁵\(\le\)3ⁿ\(\le\)3⁵

5\(\le\)n\(\le\)5

\(\Rightarrow\)n=5

a) 2.16\(\ge\)2ⁿ>4

=>2.2⁴\(\ge\)2ⁿ>4

=>2^5\(\ge\)2ⁿ>2²

^{=>5\(\ge\)n>2}

^=>n\(\in\){3,4,5}

b)9.27\(\le\)3ⁿ\(\le\)243

=>3².3³\(\le\)3ⁿ\(\le\)3⁵

=>3⁵\(\le\)3ⁿ\(\le\)3⁵

=>5^\(\le\)n\(\le\)5

=>n=5

a, \(2.16\ge2^n>4\)

\(\Leftrightarrow2.2^4\ge2^n>2^2\)

\(\Leftrightarrow2^5>2^n>2^2\)

\(\Leftrightarrow5\ge n>2\)

Vậy \(n\in\left\{3;4;5\right\}\)

b, Câu b làm tương tự nhé!

a)2^5 lớn hơn hoặc bằng 2^n lớn hơn 2^2

suy ra n=4;3

b)243 nhỏ hơn , bằng 3^n nhỏ hơn hoặc = 243

suy ra n=5

Bài làm:

\(32< 2^n< 128\) 

hay \(2^5< 2^n< 2^7\)

\(\Rightarrow n=6\)

b, \(2\cdot16\ge2^n>4\)

hay \(32\ge2^n>4\)

\(2^5\ge2^n>2^2\)

\(\Rightarrow n\varepsilon\left(3,4,5\right)\)

c, \(9\cdot27\le3^n\le243\)

hay \(63\le3^n\le243\)

\(63\le3^n\le3^5\)

=> \(n\varepsilon\left(3;4\right)\)

#chúc bạn học tốt

Sorry, mình nhầm, câu c n thuộc (4;5) sorry bạn mong bạn bỏ qua

\(a)32>2^x>128\)

\(2^5>2^x>2^7\)

\(\Rightarrow x=6\)

\(b)2.16\ge2^x\ge4\)

\(2.2^4\ge2^x\ge2^2\)

\(2^5\ge2^x\ge2^2\)

\(\Rightarrow x=5;4;3;2\)

\(c)9.27\le3^x\le243\)

\(3^2.3^3\le3^x\le3^5\)

\(3^5\le3^x\le3^5\)

\(\Rightarrow x=5\)

a: \(\Leftrightarrow2^5>2^n>2^2\)

=>2<n<5

hay \(n\in\left\{3;4\right\}\)

b: \(\Leftrightarrow3^5< =3^n< =3^5\)

=>n=5

a) ta có 2.16\(\ge\)2ⁿ > 4

    \(\rightarrow\)2.2⁴\(\ge\)2ⁿ>2²

    ^{\(\rightarrow\)} 2⁵\(\ge\)2ⁿ>2²

^{\(\Rightarrow\)} n\(\in\){ 3;4;5}

b) làm tương tự

\(2.16\ge2^n\ge4\)

\(\Rightarrow32\ge2^n>4\)

\(\Rightarrow2^5\ge2^n>2^2\)

\(\Rightarrow n\le\left\{3;4;5\right\}\)

\(2.16\ge2^n\ge4\Rightarrow2.2^4\ge2^n\ge2^2\Rightarrow2^5\ge2^n\ge2^2\Rightarrow5\ge n\ge2\Rightarrow n=\left(5;4;3;2\right)\)

a. 2.16 \(\ge\)2ⁿ>4

=> 32 \(\ge\)2ⁿ>4

=> 2⁵ \(\ge\)2ⁿ>2²

=> n \(\in\left\{3;4;5\right\}\)

b. \(9.27\le3^n\le243\)

=> \(243\le3^n\le243\)

=> \(3^5\le3^n\le3^5\)

=> n=5