自然对数的底e是一个十分重要的常数,纵观国内的竞赛试题、自主招生试题、高考试题以及高考模拟题,与常数e有关的不等式证明题推陈出新,屡见不鲜,但大多数都较难处理.面对这些问题时,很多人感觉无从下手,真所谓“不识庐山真面目,只怨分析不透彻”.本文拟对此类问题给以分析、归纳、拓展,希望达到抛砖引玉的效果.首先我们给出一个常用的指数不等式: The bottom of the natural logarithm of e is a very important constant, looking at the domestic competition test questions, self-enrollment test questions, college entrance examination questions and college entrance examination simulation questions, and the constant e inequality proves a new and common, but most are more difficult to deal with In the face of these problems, many people feel unable to start, so-called “do not know the truth, only blame the analysis is not thorough.” This paper is intended to analyze, summarize and expand such issues, hoping to achieve the desired effect. First, we give a commonly used exponential inequality: