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De Morgan's Law

Solve the fol...

Question

Solve the following inequality:
${log}_{0.5} (x^{2} - 3 x + 4) - {log}_{0.5} (x - 1) < - 1$

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Solution

$- {log}_{2} (x^{2} - 3 x + 4) + {log}_{2} (x - 1) < - 1$
$t a k e a n t i l o g, w e g o t$
$\frac{x - 1}{x^{2} - 3 x + 4} < \frac{1}{2}$
$\frac{2 x - 2 - x^{2} + 3 x - 4}{x^{2} - 3 x + 4} < 0$
$\frac{{- x}^{2} + 5 x - 6}{x^{2} - 3 x + 4} < 0$
$\frac{x^{2} - 5 x + 6}{x^{2} - 3 x + 4} < 0$
$\frac{{- x}^{2} + 5 x - 6}{x^{2} - 3 x + 4} < 0$
$\frac{x^{2} - 5 x + 6}{x^{2} - 3 x + 4} < 0$
$a s " D " f o r x^{2} - 3 x + 4 i s l e s s t h a n^{'} 0^{'}, w e c a n s a y t h a t x^{2} - 3 x + 4 > 0, x ε R$
$x^{2} - 5 x + 6 < 0$
$(x - 3) (x - 2) < 0$
$x ε (2, 3)$

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