Question

If $lo{g}_{0.5}(x-1)<lo{g}_{0.25}(x-1),$ then x lies in the interval.

• A. $(2,\infty )$
• B. $(3,\infty )$
• C. $(-\infty ,0)$
• D. (0, 3)

Answer 1

The correct option is A

$(2,\infty )$

$lo{g}_{0.5}(x-1)<lo{g}_{0.25}(x-1)\iff lo{g}_{0.5}(x-1)<lo{g}_{(0.5{)}^2}(x-1)=\frac{lo{g}_{0.5}(x-1)}{lo{g}_{0.5}(0.5{)}^2}=\frac{1}{2}lo{g}_{0.5}(x-1)\iff lo{g}_{0.5}(x-1)<0\iff x-1>1\iff xϵ(2,\infty )$