The equation e$^$x $=32$x is equivalent to the equation f$($x$)=$ ex $3+2$x $=0.$ f$($x$)$ is continuous on the interval $[0,1],$ f$(0)=2,$ and f$(1)=1\mathrm{.}718.$ Since $---$Select$---$ f$(0)$ f$(1)<0<---$Select$---$ f$(0)$ f$(1),$ there is a number c in $(0,1)$ such that f$($c$)=0$ by the Intermediate Value Theorem. Thus, there is a root of the equation ex $=32$x$,$ in the interval $(0,1).$