3:

a: 3^x*3=243

=>3^x=81

=>x=4

b; 2^x*16^2=1024

=>2^x=4

=>x=2

c: 64*4^x=16^8

=>4^x=4^16/4^3=4^13

=>x=13

d: 2^x=16

=>2^x=2^4

=>x=4

a) \(2^n:4=16\)

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

\(=>n-2=4\)

\(=>n=6\)

b) \(3^n:3^2=243\)

\(3^n:3^2=3^5\)

\(=>n-2=5\)

\(=>n=7\)

vay \(n=7\)

c) \(2^n-64=2^6\)

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

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

\(2^n=128\)

\(2^n=2^7\)

\(=>n=7\)

vay \(n=7\)

A/ => 16.4=2ⁿ

=> 2ⁿ =64

2ⁿ=2⁶

=> n = 6

B/ 3ⁿ=243.3²

3ⁿ=3⁵.3²

3ⁿ=3⁷

Vậy n = 7

a) n = 4 ; n = 5

b) n = 6 ; n = 6

c) n = 0 ; n = 6

a) \(2^n:4=16\Rightarrow2^n:2^2=2^4\Rightarrow2^{n-2}=2^4\Rightarrow n-2=4\Rightarrow n=6\)

b) \(6\cdot2^n+3\cdot2^n=9\cdot2^9\)

=> \(\left(6+3\right)\cdot2^n=9\cdot2^9\)

=> \(9\cdot2^n=9\cdot2^9\Rightarrow n=9\)

c) \(3^n:3^2=243\)

=> \(3^{n-2}=3^5\)

=> n - 2 = 5 => n = 7

d) 25 < 5ⁿ < 3125

=> 5² < 5ⁿ < 5⁵

=> n \(\in\){3;4}

a) n=10

b) 2

k nha

a) n = 2 

b)n = 2

a>2^n=16=>2^n=2^4 =>n=4

   3^n=243=> 3^n=3^5 =>n=5

 b>4^n=4096 =>4^n=4^6=>n=6

     5^n=15625 =>5^n=5^6 =>n=6

c>6^n+3=216 =. 6^n+3=6^3 =>n+3=3

                                              n=0

   4^n-1=1024 =>4^n-1=4^5 =>n-1=5

                                             n=4

Chuc ban vao nam hoc dc nhieu may man!!

a) \(\dfrac{81}{\left(-3\right)^n}=-243\)

\(\dfrac{\left(-3\right)^4}{\left(-3\right)^n}=\left(-3\right)^5\)

\(\left(-3\right)^n=\dfrac{\left(-3\right)^4}{\left(-3\right)^5}=\left(-3\right)^{-1}\)

n = -1

Vậy n = -1

b) \(\dfrac{25}{5^n}=5\)

\(\dfrac{5^2}{5^n}=5^1\)

\(5^n=\dfrac{5^2}{5^1}=5^1\)

n = 1

Vậy n = 1

c) \(\dfrac{1}{2}\cdot2^n+4\cdot2^n=9\cdot2^5\)

\(2^{n-1}+4\cdot2^{n-1}\cdot2=9\cdot2^5\)

\(2^{n-1}+8\cdot2^{n-1}=9\cdot2^5\)

\(\left(8+1\right)\cdot2^{n-1}=9\cdot2^5\)

\(9\cdot2^{n-1}=9\cdot2^5\)

\(2^{n-1}=2^5\cdot\dfrac{9}{9}=2^5\)

n - 1 = 5

n = 5 + 1 = 6

Vậy n = 6

a) 81/(-3)ⁿ = -243

(-3)ⁿ = 81 : (-243)

(-3)ⁿ = -1/3

n = -1

b) 25/5ⁿ = 5

5ⁿ = 25 : 5

5ⁿ = 5

n = 1

c) 1/2 . 2ⁿ + 4 . 2ⁿ = 9 . 2⁵

2ⁿ . (1/2 + 4) = 9 . 32

2ⁿ . 9/2 = 288

2ⁿ = 288 : 9/2

2ⁿ = 64

2ⁿ = 2⁶

n = 6