Solve ${log}_{0.3} (x^{2} - x + 1) > 0$ .

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Solution

${log}_{0.3} (x^{2} - x + 1) > 0$ or $0 < x^{2} - x + 1 < {(0.3)}^{0}$
or $0 < x^{2} - x + 1 < 1 \Rightarrow x^{2} - x + 1 > 0$ and $x^{2} - x < 0$
or $x (x - 1) < 0$
$\Rightarrow$ $0 < x < 1$ .... (as $x^{2} - x + 1 = {(x - \frac{1}{2})}^{2} + \frac{3}{4} > 0$ ), for all real x
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