Question

log (x - 2) na base 5 = log ( - x² + 4) na base 5

Gabarito: 

Answer 1

Resposta:

Explicação passo-a-passo:

log₅(x-2)=log₅(-x²+4)

x-2= -x²+4

x²+x-6=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+1x-6=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=1~e~c=-6\\\\\Delta=(b)^{2}-4(a)(c)=(1)^{2}-4(1)(-6)=1-(-24)=25\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(1)-\sqrt{25}}{2(1)}=\frac{-1-5}{2}=\frac{-6}{2}=-3\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(1)+\sqrt{25}}{2(1)}=\frac{-1+5}{2}=\frac{4}{2}=2\\\\S=\{-3,~2\}$