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Question

If $$\log_{0.3} (x -1) < \log_{0.09} (x -1)$$, then $$x$$ lies in the interval


A
x(0,)
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B
x(1,)
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C
x(2,)
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D
x(3,)
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Solution

The correct option is C $$x \in (2,\infty)$$
$$\log_{0.3} (x-1) < \log _{0.09} (x - 1)$$
$$\Rightarrow \log_{0.3} (x -1)- \dfrac{1}{2} \log_{0.3} (x - 1) < 0$$
$$\Rightarrow \log_{0.3} (x - 1) < 0$$
$$ x - 1 > 1$$, as $$ 0 <$$ base $$< 1$$
$$x > 2 $$

Mathematics

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