Log of negative numbers

I know that log of negative numbers is complex numbers. But I just got over this little proof and wondering what is wrong with this?

$\mathrm{log}(-a)=\frac{2\times \mathrm{log}(-a)}{2}=\frac{1}{2}\mathrm{log}\left({a}^{2}\right)=\frac{2}{2}\mathrm{log}\left(a\right)=\mathrm{log}\left(a\right)$

I know that log of negative numbers is complex numbers. But I just got over this little proof and wondering what is wrong with this?