complex Numbers

If $ log _{\frac{1}{2}}\frac{[|z|^2 +2|z|+4}{[2|z|^2+1]]}<0 $, then the region traced by z is
i) $ |z|<3 $
ii) $ 1<|z|<3 $
iii) $ |z|>1 $
iv) $ |z|<2 $

Please show the working. I'm more interested in knowing the procedure.

Thanks in advance.

$$\frac{|z|^2 +2|z|+4}{2|z|^2+1}>1$$
$$|z|<3$$

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