a)1/9.27^n=3^n

             3^n=3^n

         =>n={0;1;2;3;...}     

a) n= 2;3;5;7;...(n là số nguyên)

 a)1/9.27^n=3^n

 3^n=3^n

=>n={0;1;2;3...}

 Tích nha ^_^ !!!

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: \(32^{-n}.16^n=2048\)

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

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

\(\Rightarrow4n=5n+11\)

\(\Rightarrow n=-11\)

Bài 1 :

a) 7^2x-1 = 343

=> 7^2x-1 = 7³

=> 2x - 1 = 3 => 2x = 4 => x = 2

b) (7x - 11)³ = 2⁵.3² + 200

=> (7x - 11)³ = 32.9 + 200

=> (7x - 11)³ = 488

xem kĩ lại đề này :vvv

c) 174 - (2x - 1)² = 5³

=> (2x - 1)² = 174 - 5³

=> (2x - 1)² = 174 - 125 = 49

=> (2x - 1)² = (\(\pm\)7)²

=> \(\orbr{\begin{cases}2x-1=7\\2x-1=-7\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=-3\end{cases}}\)

Mà x \(\in\)N nên x = 4( thỏa mãn điều kiện)

Bài 2 :

a) x⁵ = 32 => x⁵ = 2⁵ => x = 2

b) (x + 2)³ = 27

=> (x + 2)³ = 3³

=> x + 2 = 3 => x = 3 - 2 = 1

c) (x - 1)⁴ = 16

=> (x - 1)⁴ = 2⁴

=> x - 1 = 2 => x = 3 ( vì đề bài cho x thuộc N nên thỏa mãn)

d) (x - 1)⁸ = (x - 1)⁶

=> (x - 1)⁸ - (x - 1)⁶ = 0

=> (x - 1)⁶ [(x - 1)² - 1] = 0

=> \(\orbr{\begin{cases}\left(x-1\right)^6=0\\\left(x-1\right)^2-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\\left(x-1\right)^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\\left(x-1\right)^2=\left(\pm1\right)^2\end{cases}}\)

+) x - 1 = 1 => x = 2 ( tm)

+) x - 1 = -1 => x = 0 ( tm)

Vậy x = 1,x = 2,x = 0

 a) 5^3 = 125

b)3^4.3^3=3^7

c)27.3^2=243

d)49.7^2=2401

e) chịu -_-

a)

1/9 . 3^4.3ⁿ=3⁷

=>3^-2.3^4.3ⁿ=3⁷

=>3^-2+4+n=3⁷

=>-2+4+n=7

=>n=7-(-2)-4

=>n=5

a) \(9.27^n=3^5\Rightarrow3^2.\left(3^3\right)^n=3^5\)

\(\Rightarrow3^2.3^{3n}=3^5\Rightarrow3^{5n}=3^5\)

\(\Rightarrow5n=5\Rightarrow n=1\)

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

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

\(\Rightarrow1+n=2\Rightarrow n=1\)

c)\(3^2.3^4.3^n=3^7\Rightarrow3^{6+n}=3^7\)

\(\Rightarrow6+n=7\Rightarrow n=1\)

d)\(2^{-1}.2^n+4.2^n=9.2^5\)

\(\Rightarrow2^n\left(2^{-1}+4\right)=3^2.2^5\)

\(\Rightarrow\)\(2^n\left(\frac{1}{2}+4\right)=3^2.2^5\)

\(\Rightarrow\)\(2^n.\frac{3^2}{2}=3^2.2^5\)

\(\Rightarrow\)\(2^{n-1}.3^2=3^2.2^5\)

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

e)\(243\ge3^n\ge9.3^2\)

\(\Rightarrow3^5\ge3^n\ge3^2.3^2\)

\(\Rightarrow3^5\ge3^n\ge3^4\)

\(\Rightarrow5\ge n\ge4\Rightarrow5;4\)

f)\(2^{n+3}.2^n=128\)

\(\Rightarrow2^{n+3+n}=2^7\)

\(\Rightarrow2^{2n+3}=2^7\)

\(\Rightarrow2n+3=7\Rightarrow2n=4\Rightarrow n=2\)

Hok tối

a. n = 4

A. 3^n=3^4

        n=4

b.5^n=125

   5^n=5^3

      n=3

a,\(3^n\)=81

3^n = 3^4

=> n = 4

b,5^n=125

5^n = 125

5^n = 5^3

=> n = 3

c,2^3.2^4=64

Sai đề nhé!

d,7.7^n+1=343

7.7^n+1 = 7^3

7^n+1 = 7^3:7 

7^n+1 = 7^2

n+1 = 2 => n = 1

e,2.3^n=162

3^n = 162:2

3^n = 3^4

=> n = 4

g,49.7^n=2401

7^2.7^n = 7^4

7^n = 7^4:7^2

7^n = 7^2 => n= 2