Question

The number of solution of ${\log }_e|x|=\sqrt{2-x^2}$ is

• A. $4$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $4$

$\begin{array}{c}{\log }_e\left|x\right|=\sqrt{2-x^2}\\ \Rightarrow \left|x\right|>0and2-x^2\ge 0\\ x>0\\ \Rightarrow {\left(\sqrt{2}\right)}^2-x^2\ge 0\\ \Rightarrow \left(\sqrt{2}-x\right)\left(x+\sqrt{2}\right)\ge 0\\ and\Rightarrow \left|x\right|\ne 1\end{array}$

Hence, number of solution is (4).