Question

b)log 2 (2x + 3) = log 2 x 2

Answer 1

Resposta:

x= -1 ou x=3

Explicação passo-a-passo:

log₂(2x+3)=log₂x²

2x+3=x²

x²-2x-3=0

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-2x-3=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-2~e~c=-3\\\\\Delta=(b)^{2}-4(a)(c)=(-2)^{2}-4(1)(-3)=4-(-12)=16\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-2)-\sqrt{16}}{2(1)}=\frac{2-4}{2}=\frac{-2}{2}=-1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-2)+\sqrt{16}}{2(1)}=\frac{2+4}{2}=\frac{6}{2}=3\\\\S=\{-1,~3\}$

Para x= -1

log₂(2(-1)+3)=log₂(-1)²

log₂(-2+3)=log₂1

log₂1=log₂1 (VERDADEIRO)

Para x=3

log₂(2(3)+3)=log₂(3)²

log₂(6+3)=log₂9

log₂9=log₂9 (VERDADEIRO)