Question

The number of real roots of equation ${\log }_{e}x+ex=0$

• A. $0$ (Zero)
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

${\log }_{e}x+ex=0\cdots \left(1\right)$
$\Rightarrow {\log }_{e}x=-ex$

We can simply draw the graphs of $y={\log }_{e}x$ and $y=-ex$ and their number of intersections with each other will give us the number of real roots of the equation $\left(1\right)$

From the graph, there is only one root of the given equation.