If {log _{tan {{30}^ circ }}}left( {fra | vedclass

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Question

$\log _{\frac{1}{\sqrt{3}}}\left(\frac{2|z|^{2}+2|z|-3}{|z|+1}\right)<-2$

$\Rightarrow \frac{2|z|^{2}+2|z|-3}{|z|+1}>\frac{2|z|^{2}+2|z|-3}{|

Vedclass · Accepted Answer

$\left| z \right|\, > {2}$

Vedclass · Answer

$\log _{\frac{1}{\sqrt{3}}}\left(\frac{2|z|^{2}+2|z|-3}{|z|+1}\right)<-2$

$\Rightarrow \frac{2|z|^{2}+2|z|-3}{|z|+1}>\frac{2|z|^{2}+2|z|-3}{|z|+1}>\left(\frac{1}{\sqrt{3}}\right)^{-2}$

$\frac{2|z|^{2}+2|z|-3}{|z|+1}>3 $

$\Rightarrow 2|z|^{2}-|z|-6>0$

$\Rightarrow|z|>2$

If ${\log _{\tan {{30}^ \circ }}}\left( {\frac{{2{{\left| z \right|}^2} + 2\left| z \right| - 3}}{{\left| z \right| + 1}}} \right)\, < \, - 2$ then

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