a, \(\dfrac{16}{2^n}=2\)

\(2^n=\dfrac{16}{2}\)

\(2^n=8\)

\(2^n=2^3\)

=> n = 3

b, \(\dfrac{\left(-3\right)^n}{81}=-27\)

\(\left(-3\right)^n=-27\cdot81\)

\(\left(-3\right)^n=\left(-3\right)^3\cdot3^4\)

\(\left(-3\right)^n=\left(-3\right)^7\)

=> n = 7

c, \(8^n:2^n=4\)

\(2^{3n}:2^n=2^2\)

\(2^{2n}=2^2\)

=> 2n = 2

n = 2:2

n = 1

a )

\(\dfrac{16}{2^n}=2\) \(\Leftrightarrow16:x=2\)

\(\Rightarrow x=8\)

\(2^n=8\Rightarrow n=3\)

b )

\(\dfrac{\left(-3\right)^n}{81}=-27\) \(\Leftrightarrow x=-27.81\)

\(\Rightarrow x=-2187\)

\(\left(-3\right)^n=-2187\Rightarrow n=7\)

c )

\(8^n:2^n=4\Leftrightarrow4^n=4\)

\(\Rightarrow n=1\)

(2^2:4)*2^n=4

3^2*3^4*3^n=3^7

Bài 1:

a, \(\left(x-2\right)^2=9\)

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

b, \(\left(3x-1\right)^3=-8\)

\(\Rightarrow3x-1=-2\Rightarrow3x=-1\)

\(\Rightarrow x=-\dfrac{1}{3}\)

c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)

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

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

d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\)

\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^2\)

Vì \(\dfrac{2}{3}\ne\pm1;\dfrac{2}{3}\ne0\) nên \(x=2\)

e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{x-1}=\left(\dfrac{1}{2}\right)^4\)

Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(x-1=4\Rightarrow x=5\)

\(a,\frac{16}{2^n}=2\Rightarrow2^n=16:2\Rightarrow2^n=8\Rightarrow2^n=2^3\Rightarrow n=3\)

\(b,\frac{\left(-3\right)^n}{81}=-27\Rightarrow\left(-3\right)^n=81.\left(-27\right)\Rightarrow\left(-3\right)^n=-2187\Rightarrow3^n=3^7\Rightarrow n=7\)

\(c,8^n:2^n=4\Rightarrow4^n=4\Rightarrow n=1\)

\(a,\frac{16}{2^n}=2\)                                    \(b,\frac{\left(-3\right)^n}{81}=-27\)                                              \(c,8^n:2^n=4\)

\(\Rightarrow2^4=2^n.2\)                                 \(\Rightarrow\left(-3\right)^n=\left(-27\right).81\)                                \(\Rightarrow\left(8:2\right)^n=4\)

\(\Rightarrow4=n+1\)                                 \(\Rightarrow\left(-3\right)^n=\left(-3\right)^7\)                                        \(\Rightarrow4^n=4\)

\(\Rightarrow n=4-1=3\)                         \(\Rightarrow n=7\)                                                                \(\Rightarrow n=1\)

a)x ∈ ∅

b) x=3

\(a,\Rightarrow2^3< 2^x\le2^4\Rightarrow x=4\\ b,\Rightarrow3^3< 3^{12}:3^x< 3^5\\ \Rightarrow3^3< 3^{12-x}< 3^5\\ \Rightarrow12-x=4\Rightarrow x=8\)

a. \(\dfrac{32}{2^n}=2\)

\(\Leftrightarrow2^n.2=32\)

\(\Rightarrow2^{n+1}=2^5\)

\(\Rightarrow n+1=5\)

\(\Rightarrow n=4\)

Vậy...

b. \(16^n:2^n=8\)

\(\Rightarrow\left(2^4\right)^n:2^n=2^3\)

\(\Rightarrow4n-n=3\)

\(\Rightarrow3n=3\)

\(\Rightarrow n=1\)

Vậy...

c. \(\dfrac{\left(-3\right)^n}{81}=\left(-27\right)\)

\(\Leftrightarrow\left(-3\right)^n=81.\left(-27\right)\)

\(\Rightarrow\left(-3\right)^n=\left(-2187\right)\)

\(\Rightarrow\left(-3\right)^n=\left(-3\right)^7\)

\(\Rightarrow n=7\)

Vậy...

a, \(\dfrac{32}{2^n}\) =2 =>2⁵=2ⁿ⁺¹=>5=n+1=>n=4

b, 2⁴ⁿ:2ⁿ=2³=>2³ⁿ=2³=>3n=3=>n=1

c, \(\dfrac{\left(-3\right)^n}{81}\)=(-27)=>(-3)ⁿ=3⁴ . (-3)³=>n=7

\(a,\frac{16}{2^n}=2=>\frac{2^4}{2^n}=2=>2^4:2^n=2=>2^{4-n}=2=>4-n=1=>n=3\)

\(b,\frac{\left(-3\right)^n}{81}=-27=>\frac{\left(-3\right)^n}{3^4}=\left(-3\right)^3=>\frac{\left(-3\right)^n}{\left(-3\right)^4}=\left(-3\right)^3=>\left(-3\right)^{n-4}=\left(-3\right)^3=>n-4=3=>n=7\)

\(c,8^n:2^n=4=>\left(8:2\right)^n=4=>4^n=4=>n=1\)

mk đã làm r nhé bn

a) \(2\left(\dfrac{2}{3.5}+\dfrac{4}{5.9}+...+\dfrac{16}{n\left(n+16\right)}\right)=\dfrac{16}{25}\)

\(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n}-\dfrac{1}{n+16}=\dfrac{8}{25}\)

\(\dfrac{1}{3}-\dfrac{1}{n+16}=\dfrac{8}{25}\)

\(\dfrac{n+13}{3\left(n+16\right)}=\dfrac{8}{25}\)

\(24n+384=25n+325\)

\(25n-24n=384-325\)

\(n=59\)

b) Sai đề nha

\(\left\{{}\begin{matrix}\dfrac{2018}{2019}< 1\\\dfrac{2019}{2020}< 1\\\dfrac{2020}{2021}< 1\\\dfrac{2021}{2022}< 1\end{matrix}\right.\)

\(\Rightarrow\dfrac{2018}{2019}+\dfrac{2019}{2020}+\dfrac{2020}{2021}+\dfrac{2021}{2022}< 4\)

chị ơi hình như chị nhầm rồi P/s cuối phải là 1/n.(n+6)thì phải

a) \(\frac{16}{2^n}=2\)

=> 16 = 2 . 2ⁿ 

=> 16 = 2ⁿ⁺¹

=> 2⁴ = 2ⁿ⁺¹

=> n + 1 = 4

=> n = 4 - 1

=> n = 3

Vậy n = 3

b) \(\frac{\left(-3\right)^n}{81}=-27\)

=> (-3)ⁿ = -27 . 81

=> (-3)ⁿ = (-3)³ . (-3)⁴

=> (-3)ⁿ = (-3)⁷

=> n = 7

Vậy n = 7

c) 8ⁿ : 2² =  bao nhiêu vậy ban?

Chuk bn hk tốt!

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

    \(\Rightarrow16:2=2^n\) 

         2ⁿ=8=2³

Vậy n=3

b)\(\frac{\left(-3\right)^n}{81}=-27\)

  \(\Rightarrow\)(-3)ⁿ=-27.81

      (-3)ⁿ=-2187=(-3)⁷

Vậy n=7

c)Mk ko hiểu bn ghi gì

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

\(\Rightarrow2^n=\frac{16}{2}=8=2^3\)

\(\Rightarrow n=3\)

b) \(\frac{\left(-3\right)^n}{81}=27\)

\(\Rightarrow\left(-3\right)^n=-27.81=-2187=\left(-3\right)^7\)

\(\Rightarrow n=7\)
c) thiếu đề