Why does the same inequality give different answers?

$({\mathrm{log}}_{2}\left(x\right)-2)({\mathrm{log}}_{2}\left(x\right)+1)<0$

has a solution $\frac{1}{2}<x<4$

But when we take the second part alone that is

$({\mathrm{log}}_{2}\left(x\right)+1)<0$

it gives a solution $0<x<\frac{1}{2}$ why is $x>\frac{1}{2}$ in the first case but $x<\frac{1}{2}$ in the second case?

$({\mathrm{log}}_{2}\left(x\right)-2)({\mathrm{log}}_{2}\left(x\right)+1)<0$

has a solution $\frac{1}{2}<x<4$

But when we take the second part alone that is

$({\mathrm{log}}_{2}\left(x\right)+1)<0$

it gives a solution $0<x<\frac{1}{2}$ why is $x>\frac{1}{2}$ in the first case but $x<\frac{1}{2}$ in the second case?