The-area-of-the-region-in-the-complex-plane-satisfying-the-inequality-log-cos-pi-6-z-2-5-4-z-2-4-lt-2-is-

Question Number 139057 by EnterUsername last updated on 21/Apr/21

The area of the region in the complex plane satisfying

the inequality \log_{\cos (\frac{π}{6})} [\frac{∣ z - 2 ∣ + 5}{4 ∣ z - 2 ∣ - 4}] < 2 is ?

Answered by MJS_new last updated on 22/Apr/21

∣ z - 2 ∣= x ⩾ 0

\frac{\ln \frac{x + 5}{4 (x - 1)}}{\ln \cos \frac{π}{6}} < 2 \Leftrightarrow \ln \frac{x + 5}{x - 1} > \ln 3

\frac{x + 5}{x - 1} > 3 \Rightarrow x < 4

0 ⩽ x < 4

0 ⩽∣ z - 2 ∣< 4

this is a circle with center (\begin{matrix} 2 \\ 0 \end{matrix}) and radius 4

but without the circle line

Commented by EnterUsername last updated on 22/Apr/21

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