Question

a) \(\left(14^{x-1}\right)^2=196\)

b)\(3^x+3^{x+1}+3^{x+2}=39\)

c) \(\left(3x-7\right)^{2012}=\left(3x-7\right)^{2013}\)

Answer 1

`a, (14^(x - 1))^2 = 196`

`(14^(x - 1))^2 = 14^2`

`14^(2x - 2) = 14^2`

`2x - 2 = 2`

`2x = 2 + 2`

`2x = 4`

`x = 4:2`

`x= 2`

Vậy: `x = 2`

`b, 3^x + 3^(x + 1) + 3^(x + 2) = 39`

`3^x + 3^x . 3 + 3^x . 3^2 = 39`

`3^x .(1 + 3 + 3^2) = 39`

`3^x . 13 = 39`

`3^x = 39 :13`

`3^x = 3`

`3^x = 3^1`

`x = 1`

Vậy: `x=1`

 

Answer 2

`c, (3x - 7)^2012 = (3x - 7)^2013`

`(3x - 7)^2012 - (3x - 7)^2013 = 0`

`(3x - 7)^2012 . [1 - (3x - 7)] = 0`

`(3x - 7)^2012 . (1 - 3x + 7) = 0`

`(3x - 7)^2012 . (8 - 3x) = 0`

`(3x - 7)^2012 = 0` hoặc `8 - 3x = 0`

`3x - 7 = 0` hoặc `3x = 8 - 0`

`3x = 7` hoặc `3x = 8`

`x = 7 : 3` hoặc `x = 8 : 3`

`x = 7/3` hoặc `x = 8/3`

Vậy: `x = 7/3; x = 8/3`