Question

(UDESC) Resolva a equação Log(x-1) (2x^2-7x+7)=0

Answer 1

$\log_{x-1}(2x^2-7x+7)=0$

$2x^2-7x+7=(x-1)^0$

$2x^2-7x+7=1$

$2x^2-7x+6=0$

$x=\frac{-(-7)\pm\sqrt{(-7)^2-4\cdot2\cdot6}}{2\cdot2}$

$x=\frac{7\pm1}{4}$

$x\in\{\frac{3}{2},2\}$

Answer 2

De acordo com a definicao de Logaritmos,

X = 2 ou X = 3/2