Question

if \(\log _{0.3}(x-1)<\log _{009}(x-1)\), then \(x\) lies in the interval
(A) \((2, \infty)\)
(B) \((1,2)\)
(C) \((-2,-1)\)
(D) None of these

Answer 1

Ans : (A)
 \(: \log _{03}(x-1)<\log _{(0.3)}^{2}(x-1) \Rightarrow \log _{03}(x-1)^{2}<\log _{(03)}(x-1) \Rightarrow(x-1)^{2}>x-1 \quad(0.3<1)\)
\(\Rightarrow(x-1)(x-2)>0 \Rightarrow x<1, x>2 \Rightarrow x>2 \quad(x \neq 1)\)