Question

Tìm n\(\in\)\(ℕ^∗\)biết

a, \(3^2.3^n=3^5\)

b, \(\left(2^2:4\right).2^n=4\) 

c, \(\frac{1}{9}.3^4.3^n=3^7\)

d,\(\frac{1}{9}.27^n=3^n\)

Answer 1

a) 3² . 3ⁿ = 3⁵

=> 3ⁿ      = 3⁵ : 3²

=> 3ⁿ      = 3³

=>   n      = 3

b) (2² :  4) . 2ⁿ = 4

=> (4 : 4) . 2ⁿ   = 4

=> 2ⁿ                = 4

=> 2ⁿ                = 2²

=>   n                = 2

c) \(\frac{1}{9}.3^4.3^n=3^7\) 

\(\Rightarrow3^{-2}.3^4.3^n=3^7\)

\(\Rightarrow3^{-2+4+n}=3^7\)

\(\Rightarrow3^{2+n}=3^7\)

\(\Rightarrow2+n=7\)

\(\Rightarrow n=5\)

d) \(\frac{1}{9}.27^n=3^n\)

\(\Rightarrow3^{-2}.3^{3n}=n\)

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

\(\Rightarrow-2+3n=n\)

\(\Rightarrow2n=2\)

\(\Rightarrow n=1\)

Answer 2

Bài làm :

a) 3² . 3ⁿ = 3⁵

3ⁿ = 3⁵ : 3²

3ⁿ = 3³

=> n = 3

Vậy n = 3

b) ( 2² : 4 ) . 2ⁿ = 4

( 4 : 4 ) . 2ⁿ = 4

=> 2ⁿ = 4

=> n = 2

Vậy n = 2

2 phần cuối bạn tham khảo bạn dưới nhé / Tiểu Dã /

Answer 3

a) \(3^2.3^n=3^5\Rightarrow3^n=3^5:3^2=3^3\Rightarrow x=3\)

b) \(\left(2^2:4.\right).2^n=4\Rightarrow1.2^n=4\Rightarrow2^n=4\Rightarrow n=2\)

c)\(\frac{1}{9}.3^4.3^n=3^7\Rightarrow4+n-3=7\Rightarrow n=7+3-4=6\)