Question

14. Resolver: Log(x - 1) + Log(x - 2) = 2
a) 1
d)-2
c) 3
b) o
e) -3 nada tonterías absurdas ​

Answer 1

Respuesta:

$Log(x - 1) + Log(x - 2) = 2 \\ log((x-1)\times(x-2))\\{10}^{ log((x-1)\times(x-2))} = {10}^{2} \\ (x - 1) (x - 2) = 100 \\ {x}^{2} - 2x -x +2 = 100 \\ {x}^{2} -3x= 100-2 \\ {x}^{2} -3x-98= 0 \\ \frac{-(-3)+ \sqrt{ {-3}^{2} -4(1)(-98)} }{2(1)} \\ \frac{3+ \sqrt{ 9 +392} }{2} \\\frac{3+ \sqrt{ 401} }{2} \\ x=11.5\\ \frac{-(-3)- \sqrt{ {-3}^{2} -4(1)(-98)} }{2(1)} \\ \frac{3-\sqrt{ 9 +392} }{2} \\\frac{3-\sqrt{ 401} }{2}\\ x=-8.5$