Question

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

• A. $1$
• B. $2$
• C. $0$
• D. none of these

Answer 1

The correct option is A $1$

consider the given equation.

${\log }_{0.5}x=|x|$

We know that the domain of log function is only positive x.

Therefore,

${\log }_{0.5}x=x$

Draw a graph and it is cleared that ${\log }_{0.5}x$ and $x$ intersect only one point.

Therefore, the above equation has only one real solution.

Hence, option a is correct.