Question

If $\log _{0.5}(2 x-1)<\log _{0.25}(2 x-1)$, then $x$ lies in the interval $

• A. \left(-\infty, \frac{1}{2}\right) \cup(1, \infty)
• B. \left(\frac{1}{2}, \infty\right)$
• C. $\left(\frac{1}{2}, 1\right)$
• D. $(1, \infty)$

Answer 1

Answer: (D)

$\log _{0.5}(2 x-1)<\frac{1}{2} \log _{0.5}(2 x-1) [(2 x-1)>0]$
$2 \log _{0.5}(2 x-1)<\log _{0.5}(2 x-1)$
$(2 x-1)^2 >(2 x-1) $
$(2 x-1) >1 $
$x >1 $