Question

The number of solution(s) of the equation $\text{sgn}\left(\ln x\right)=3$ is
(Here, sgn denotes the signum function)

• A. $3$
• B. $4$
• C. $0$
• D. $2$

Answer 1

The correct option is C $0$

$\text{sgn}\left(\ln x\right)=\left\{\begin{array}{c}-1,\ln x<0\\ 0,\ln x=0\\ 1,\ln x>1\end{array}\right\}\Rightarrow \text{sgn}\left(\ln x\right)=\left\{\begin{array}{c}-1,0<x<1\\ 0,x=1\\ 1,1<x<\infty \end{array}\right\}$
$\therefore \text{sgn}\left(\ln x\right)=3$ has no solution