Solution
= Solution
At a single point of contact the line is a <tangent line>, so its slope equals the <derivative> of the <exponential function>. At the contact coordinate $x_0$,
$$
m=e^{x_0},\qquad mx_0=e^{x_0}.
$$
Since $m>0$, dividing gives $x_0=1$, hence \b[$m=e$]. To verify uniqueness, the difference $e^x-ex$ has positive second <derivative> everywhere and its unique minimum is zero at $x=1$. Thus this line touches the curve once.