Từ đề bài suy ra 2⁴ ≤  2³ⁿ ≤  2⁶, tìm được n = 2

a) \(25< 5^n< 625\)

\(25=5^2;625=5^4\)

=> \(5^2< 5^n< 5^4\)

=> 2 < n < 4

=> n = 3

b) \(9\le3^n< 3.27\)

\(9=3^2;3.27=3.3^3=3^4\)

=> \(3^2\le3^n< 3^4\)

=> n = 2; hoặc n = 3

c) \(16\le8^n\le64\)

\(16=8.2;64=8^2\)

=> \(8.2\le8^n\le8^2\)

=> n = 2

\(\frac{1}{8}.16^n=2^n\)

\(\frac{1}{8}\).16ⁿ = 2ⁿ

\(\Rightarrow\)\(\frac{1}{8}\)= \(\frac{2^n}{16^n}\)

\(\Rightarrow\)\(\frac{1}{8}\)=  \(\frac{1}{8^n}\)

\(\Rightarrow\)8 = 8ⁿ

\(\Rightarrow\)n = 1

Vậy n=1

\(\frac{1}{8}.16^n=2^n\)

\(\frac{16^n}{8}=2^n\)

\(\frac{2^{4n}}{2^3}=2^n\)

\(2^{4n-3}=2^n\)

\(\Rightarrow4n-3=n\)

\(\Rightarrow4n-n=3\)

\(\Rightarrow3n=3\)

\(\Rightarrow n=1\)

vậy \(n=1\)

`1/8 xx 16^n =2^n`

`1/(2^3) xx (2^4)^n =2^n`

` 2^(-3) xx 2^(4n) =2^n`

` 2^(4n-3) =2^n`

`4n-3=n`

`3n=3`

`n=1` 

(1/32)ⁿ.16ⁿ=1024^-1

=> (1/32.16)ⁿ=1/1024

=> (1/2)ⁿ=1/1024

=> (1/2)ⁿ=(1/2)¹⁰

=> n=10

\(\left(\frac{1}{32}\right)^n.16^n=1024^{-1}\)

\(\left(\frac{1}{32}.16\right)^n=\frac{1}{1024}\)

\(\left(\frac{1}{2}\right)^n=\frac{1}{1024}\)

\(\frac{1^n}{2^n}=\frac{1}{1024}\)

<=> 1ⁿ = 1 => n thuộc N

<=> 2ⁿ = 1024

=> 2ⁿ = 1024 = 2¹⁰ ( 2ⁿ = 2¹⁰ )

<=> n = 10

5³ⁿ.5^{3n + 5}.5⁴ \(\le\)10¹⁶ : 2¹⁶

5^{6n + 9} \(\le\)5¹⁶

6n + 9 \(\le\) 16

6n \(\le\)7 \(\Rightarrow\)n < 2 \(\Rightarrow\)n =1

\(\frac{1}{8}.16^n=2^n\)

\(\Rightarrow\frac{1}{8}=2^n:16^n\)

\(\Rightarrow\frac{1}{8}=\left(\frac{2}{16}\right)^n\)

\(\Rightarrow\frac{1}{8}=\left(\frac{1}{8}\right)^n\)

\(\Rightarrow n=1\)

Vậy n=1