Question

The number of real solutions of the equation ${\log }_{0.5}x=|x|$ is

• A. $0$
• B. $1$
• C. $2$
• D. $noneofthese$

Answer 1

The correct option is B $1$

The number of real solutions of the equation ${\log }_{a}x=|x|$ is equal to the number of points of intersection of the curves.
$y={\log }_{a}x$ and $y=|x|(0<a<1)$
It is evident from the graph that the two curves intersect at one point only.
$\therefore$ One real solution lying in $(0,1)$.
Hence, $\left(b\right)$ is the correct answer.