Question

If ${\log }_{0.5}(2x-1)<{\log }_{0.25}(2x-1)$, 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)

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