a.32<2ⁿ<128

2⁵<2ⁿ<2⁷

=> n=6

b.32>2ⁿ>4

2⁵>2ⁿ>2²

=> n=3; n=4

c. 9.27<3ⁿ<243

243<3ⁿ<243

3⁵<3ⁿ<3⁵

=> không tồn tại n

32 < 2n < 128 => 16 < n < 64

=2.16<2n<2.64

suy ra:16<n<64

các bạn làm nốt dùm mk nha!

ta có 2^5<2^n<2^7

=>5<n<7

vì n là số nguyên dương 

=>n=6 

32<2n<128

2x16<2n<2x64

=> 16<n<64

Mà n thuộc N nên n thuộc {17;18;19;...;63}

(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

C

C

Bài 1:

a. $2^{29}< 5^{29}< 5^{39}$

$\Rightarrow A< B$

b.

$B=(3^1+3^2)+(3^3+3^4)+(3^5+3^6)+...+(3^{2009}+3^{2010})$

$=3(1+3)+3^3(1+3)+3^5(1+3)+...+3^{2009}(1+3)$

$=(1+3)(3+3^3+3^5+...+3^{2009})$

$=4(3+3^3+3^5+...+3^{2009})\vdots 4$

Mặt khác:

$B=(3+3^2+3^3)+(3^4+3^5+3^6)+....+(3^{2008}+3^{2009}+3^{2010})$

$=3(1+3+3^2)+3^4(1+3+3^2)+...+3^{2008}(1+3+3^2)$

$=(1+3+3^2)(3+3^4+....+3^{2008})=13(3+3^4+...+3^{2008})\vdots 13$

Bài 1:
c.

$A=1-3+3^2-3^3+3^4-...+3^{98}-3^{99}+3^{100}$

$3A=3-3^2+3^3-3^4+3^5-...+3^{99}-3^{100}+3^{101}$

$\Rightarrow A+3A=3^{101}+1$
$\Rightarrow 4A=3^{101}+1$

$\Rightarrow A=\frac{3^{101}+1}{4}$

Bài 2:

a. $7\vdots n+1$

$\Rightarrow n+1\in \left\{1; -1; 7; -7\right\}$

$\Rightarrow n\in \left\{0; -2; 6; -8\right\}$

b.

$2n+5\vdots n+1$
$\Rightarrow 2(n+1)+3\vdots n+1$

$\Rightarrow 3\vdots n+1$

$\Rightarrow n+1\in \left\{1; -1; 3; -3\right\}$

$\Rightarrow n\in \left\{0; -2; 2; -4\right\}$