Geometric visualizations of $b^{e}<e^{b}$ when $e<b$

In connection to the two fascinating constants $e$ and $π$, there are many beautiful visual proofs to the inequality $π^{e}<e^π$. The aim of this classroom capsule is to give three visual proofs to the more general inequality $b^{e}<e^{b}$ where $e<b$.

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