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Basic of Logarithms
normal
જો ${\log _{\tan {{30}^ \circ }}}\left( {\frac{{2{{\left| z \right|}^2} + 2\left| z \right| - 3}}{{\left| z \right| + 1}}} \right)\, < \, - 2$ હોય તો
A
$\left| z \right|\, < \,\frac{3}{2}$
B
$\left| z \right|\, > \,\frac{3}{2}$
C
$\left| z \right|\, > {2}$
D
$\left| z \right|\, < {2}$
Solution
$\log _{\frac{1}{\sqrt{3}}}\left(\frac{2|z|^{2}+2|z|-3}{|z|+1}\right)<-2$
$\Rightarrow \frac{2|z|^{2}+2|z|-3}{|z|+1}>\frac{2|z|^{2}+2|z|-3}{|z|+1}>\left(\frac{1}{\sqrt{3}}\right)^{-2}$
$\frac{2|z|^{2}+2|z|-3}{|z|+1}>3 $
$\Rightarrow 2|z|^{2}-|z|-6>0$
$\Rightarrow|z|>2$
Standard 11
Mathematics
