Question

Se V = {x ∈ ℝ | log(x + 2) - log(x + - 1) > log 2}, então:

a) V = ] - ∞; 1[;
b) V = ]4; +∞[;
c) V = ]-∞; 1[U] 4; + ∞[;
d) V = ]1; 4[;
e) n.d.a.​

Answer 1

Explicação passo-a-passo:

$\sf log~(x+2)-log~(x-1)>log~2$

$\sf log~\left(\dfrac{x+2}{x-1}\right)>log~2$

Devemos ter:

• $\sf \dfrac{x+2}{x-1}>2$

$\sf x+2>2\cdot(x-1)$

$\sf x+2>2x-2$

$\sf x-2x>-2-2$

$\sf -x>-4~~\cdot(-1)$

$\sf x<4$

• $\sf x+2>0~\rightarrow~x>-2$

• $\sf x-1>0~\rightarrow~x>1$

Logo:

$\sf 1 < x < 4~\rightarrow~\red{V=~]1;~4[}$

Letra D