$2^{x^{2}+1}\log _{2}(x^2+1)=4^{\left|x+1 \right|}(\log _{2}\left| {x+1} \right|+1)$
$\log _{2}\frac{\mathrm{x^{2}-x+1} }{\mathrm{2x^{2}} -4x+3}=x^{2}-3x+2$
$3x^{2}-2x^{3}=\log _{2}(x^{2}+1)-\log _{2}x$
$\log _{x^{2}}(2+x)+\log _{\sqrt{2-x}}x=2$
$\log ^{2}_{2}x+(x-1)\log _{2}x=6-2x$