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The function $f(x)=\ln x$ has an average rate of change equal to $\cfrac{3e}{e^3-1}$ on the interval $\left[\cfrac{1}{e},b \right]$ when $b=\underline{\hspace{2cm}}$

$e$

$\cfrac{1}{e}$

$\sqrt{e}$

$e^2$