Bạn tham khảo tại đây nhé: Câu hỏi của Khánh Huyền⁀ᶦᵈᵒᶫ .

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a) \(\frac{1}{9}.27^n=3^n\)

\(\Leftrightarrow3^{-2}.3^{3n}=3^n\)

\(\Leftrightarrow3^{3n-2}=3^n\)

\(\Leftrightarrow3n-2=n\)

\(\Leftrightarrow2n=2\)

\(\Leftrightarrow n=1\)

b)\(3^{-2}.3^4.3^n=3^7\)

\(\Leftrightarrow3^{2+n}=3^7\)

\(\Leftrightarrow2+n=7\)

\(\Leftrightarrow n=5\)

c) \(2^{-1}.2^n+4.2^n=9.2^5\)

\(\Leftrightarrow2^n\left(4+\frac{1}{2}\right)=9.2^5\)

\(\Leftrightarrow2^n.\frac{9}{2}=9.2^5\)

\(\Leftrightarrow2^{n-1}=2^5\)

\(\Leftrightarrow n-1=5\Leftrightarrow n=6\)

a: \(\Leftrightarrow3^n:27^n=\dfrac{1}{9}\)

\(\Leftrightarrow\left(\dfrac{1}{9}\right)^n=\dfrac{1}{9}\)

hay n=1

b: \(\Leftrightarrow3^n\cdot3^2=3^8\)

=>n+2=8

hay n=6

c: \(\Leftrightarrow2^n\cdot\dfrac{9}{2}=9\cdot2^5\)

\(\Leftrightarrow2^n=2^6\)

hay n=6

d: \(\Leftrightarrow8^n=512\)

hay n=3

a) Ta có: \(\frac{1}{9}\cdot27^n=3^n\)

\(\Leftrightarrow\frac{1}{3^2}\cdot\left(3^3\right)^n=3^n\)

\(\Leftrightarrow3^{3n}=3^{n+2}\)

\(\Rightarrow3n=n+2\)

\(\Rightarrow n=1\)

b) Ta có: \(3^2.3^4.3^n=3^7\)

\(\Rightarrow3^n=3\)

\(\Rightarrow n=1\)

c) Ta có: \(2^{-1}.2^n+4.2^n=9.2^5\)

\(\Leftrightarrow2^n\cdot\frac{9}{2}=9.2^5\)

\(\Rightarrow2^n=2^6\)

\(\Rightarrow n=6\)

d) Ta có: \(32^{-n}.16^n=2048\)

\(\Leftrightarrow\frac{1}{2^{5n}}\cdot2^{4n}=2^{11}\)

\(\Leftrightarrow2^{4n}=2^{5n+11}\)

\(\Rightarrow4n=5n+11\)

\(\Rightarrow n=-11\)

a)27ⁿ:3ⁿ=9

   (27:3)ⁿ=9

   9ⁿ=9¹

   n=1

Vậy n=1

b)\(\left(\frac{25}{5}\right)^n=5\)

    \(5^n=5^1\)

    n=1

Vạy n=1

c)\(\left(-\frac{81}{3}\right)^n=-243\)

   \(\left(-27\right)^n=\left(-3\right)^5\)

   \(\left[\left(-3\right)^3\right]^n=\left(-3\right)^5\)

   \(\left(-3\right)^{3n}=\left(-3\right)^5\)

    \(3n=5\)

   \(n=\frac{5}{3}\)

Vậy \(n=\frac{5}{3}\)

d)\(\frac{1}{2}.2^n+4.2^n=9.5^n\)

   \(2^n.\left(\frac{1}{2}+4\right)=9.5^n\)

   \(2^n.\frac{9}{2}=3^2.5^n\)

Mk làm lun, ko viết lại đề bài nữa nhé =))

a) \(\Leftrightarrow\)\(3^2.3^{n+1}=9^4\)

\(\Leftrightarrow3^{n+1}=9^4:3^2\)

\(\Leftrightarrow3^{n+1}=3^6\)

\(\Rightarrow n+1=6\)

\(\Leftrightarrow n=6-1\)

\(\Rightarrow n=5\)

b)\(\Leftrightarrow2^n.\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Leftrightarrow2^n.\frac{9}{2}=9.2^5\)

\(\Rightarrow2^n=\left(9.2^5\right):\frac{9}{2}\)

\(\Rightarrow2^n=468:\frac{9}{2}\)

Tự tính nốt KQ giúp mk nha ♥

a)1/9*3⁴*3ⁿ⁺¹=9⁴

3⁴*3ⁿ⁺¹ =9⁴/(1/9)=9⁴*9=9⁵

3⁴*3ⁿ⁺¹=3⁴⁺ⁿ⁺¹=9⁵=(3²)⁵=3¹⁰

=>4+n+1=10

n=10-4-1

Vậy n=5

b)1/2*2ⁿ+4*2ⁿ=9*2⁵

2ⁿ*(1/2+4)=9*2⁵

2ⁿ*4.5=9*2⁵

2ⁿ=9*2⁵/4.5=2⁵*2=2⁶

=> Vậy n=6

\(a)\frac{1}{9}.3^4.3^{n+1}=9^4\)

\(\Rightarrow3^{-2}.3^4.3^{n+1}=3^8\)

\(\Rightarrow3^{-2+4+n+1}=3^{n+3}=3^8\)

\(\Rightarrow n+3=8\Rightarrow n=5\)

\(b)\frac{1}{2}.2^n+4.2^n=9.2^5\)

\(\Rightarrow2^n\left(\frac{1}{2}+4\right)=9.2^5\)

\(\Rightarrow2^n.\frac{9}{2}=9.2^5\Rightarrow2^n=9.2^5.\frac{2}{9}=\frac{9.2^5.2}{9}=2^6\)

\(\Rightarrow n=6\)

a, \(\frac{1}{9}.27^n=3^n\Leftrightarrow\frac{1}{9}.3^{3.n}=3^n\Leftrightarrow\frac{1}{3^2}=3^n:3^{3n}\Leftrightarrow\frac{1}{3^2}=3^{n-3n}=3^{2n}\)

=> 3^2n . 3^2 = 1 => 3^( 2n + 2) = 3^0 => 2n + 2 = 0 => 2n = - 2 => n = - 1 

b, 3^-2.3^4 .3^n = 3^ 7 => 3^ ( -2 + 4 + n) = 3^7 => 3^ (n+ 2) = 3^7 => n + 2 = 7 => n = 5