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Definition of Ellipse

Solve the fol...

Question

Solve the following inequality:
${log}_{0.5} (3 x - 4) < {log}_{0.5} (x - 2)$

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Solution

$- {log}_{2} (3 x - 4) < - {log}_{2} (x - 2)$
${log}_{2} (3 x - 4) > {log}_{2} (x - 2)$
$3 x - 4 > x - 2$
$2 x > 2$
$x > 1$
$a n d 3 x - 4 > 0 a n d x > 2$
$x > \frac{4}{3} a n d x > 2$
$t h e r e f o r e, x ε (2, \infty)$

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