Question

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

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

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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