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Fundamental Laws of Logarithms

Find the valu...

Question

Find the value of $x$ which satisfy following equation ${log}_{0.3} (x^{2} - x + 1) > 0$ .

0 < x < 1

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1 < x < 3

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2 < x < 4

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n o n e o f t h e s e

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Solution

The correct option is C $0 < x < 1$
${log}_{0.3} (x^{2} - x + 1) > 0$ .
$\Rightarrow x^{2} - x + 1 < (.3)^{0} = 1$
$\Rightarrow x^{2} - x < 0$
$\Rightarrow x (x - 1) < 0$
$\Rightarrow 0 < x < 1$

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