Question

Tìm x, biết : 

a) \(2^{x-1}\)= 16             b,\(\left(x-1\right)^2=25\)        c,\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+6}\)và \(x\in Z\)

Answer 1

a) 2^x-1 = 16

2^x-1 = 2^4

2^x-1 = 2^5-1

=> x =5 

b) ( x-1 ) ^2 = 25

(x-1)^2 = 5^2

=> x-1 = 5

x= 5+1

x= 6

Câu c hơi dài đợi mình tí

 

Answer 2

a. 2^x-1 = 16 = 2⁴ 

=> x-1 = 4 => x=5

b. (x-1)² = 25 = 5² hoac (-5)²

=> x-1 = 5 hoac -5

=> x =  6  hoac -4

Vay: x la { 6  ; -4 }

c. (x-1)^x+2 = (x-1)^x+6                  (x la so nguyen )

=> (x-1)^x.(x-1)² = (x-1)^x . (x-1)⁶

=> (x-1)² = (x-1)⁶ 

=> (x-1)⁶:(x-1)² = (x-1)⁴ = 1

=> (x-1)⁴ = 1⁴ hoac (-1)⁴

=> x-1 = 1  hoac -1

=> x = 2  hoac 0

Vay: x la { 0 ; 2 }