Question

Tìm số tự nhiên n, biết : a) 5^n +1 = 625; b) 7^n= 7^2. 7^4; c) 7. 2^3n-1=224

 

Answer 1

`5^(n + 1) = 625`

`=> 5^(n + 1) = 5^4`

`=> n + 1      = 4`

`=> n            = 4 -1`

`=> n            = 3`

`7^n = 7^2 . 7^4`

`=> 7^n = 7^(2 + 4)`

`=> 7^n = 7^6`

`=> n = 6`

`7. 2^(3n - 1) = 224`

`=>2^(3n-1)    = 224 : 7`

`=> 2^(3n-1)  = 32`

`=> 2^(3n -1) = 2^5`

`=> 3n - 1     = 5`

`=> 3n          = 6`

`=> n            = 2`

Answer 2

a: =>5^(n+1)=5^4

=>n+1=4

=>n=3

b: =>7^n=7^6

=>n=6

c: =>2^(3n-1)=32

=>3n-1=5

=>3n=6

=>n=2

Answer 3

a) \(5^{n+1}=625\)

\(\Rightarrow5^{n+1}=5^4\)

\(\Rightarrow n+1=4\)

\(\Rightarrow n=4-1\)

\(\Rightarrow n=3\)

b) \(7^n=7^2\cdot7^4\)

\(\Rightarrow7^n=7^{2+4}\)

\(\Rightarrow7^n=7^6\)

\(\Rightarrow n=6\)

c) \(7\cdot2^{3n-1}=224\)

\(\Rightarrow2^{3n-1}=224:7\)

\(\Rightarrow2^{3n-1}=32\)

\(\Rightarrow2^{3n-1}=2^5\)

\(\Rightarrow3n-1=5\)

\(\Rightarrow3n=5+1\)

\(\Rightarrow3n=6\)

\(\Rightarrow n=\dfrac{6}{3}\)

\(\Rightarrow n=2\)