The locus of z satisfying the inequality log13z+1>log13z−1 is

w.k⇒logam>logan⇒m>nor m<nx+12+y2<x−12+y2x<0Rez<0

The locus of z satisfying the inequality log13z+1>log13z−1 is

w.k⇒logam>logan⇒m>nor m<nx+12+y2<x−12+y2x<0Rez<0

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The locus of z satisfying the inequality $\log_{\frac{1}{3}} |z + 1| > \log_{\frac{1}{3}} |z - 1|$ is

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$Im (z) > 0$

$R e (z) > 0$

$Im (z) < 0$

$R e (z) < 0$

answer is B.

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Detailed Solution

$w . k \Rightarrow \log_{a}^{m} > \log_{a}^{n} \Rightarrow m > n (o r) m < n$

${(x + 1)}^{2} + y^{2} < {(x - 1)}^{2} + y^{2}$

$x < 0$

$Re (z) < 0$

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The locus of z satisfying the inequality $\log_{\frac{1}{3}} |z + 1| > \log_{\frac{1}{3}} |z - 1|$ is