纵观近年来的试题,可以发现频频出现一类含有与自然对数lnx(或反函数e~x)相关的不等式的综合试题.这一类试题难度较大,推理繁琐、运算复杂,学生心里普遍害怕、解答时感觉棘手,甚至产生恐惧情绪,导致得分率极低.以下先证明一个大家熟知的简单的不等式:lnx≤x-1.证明:构造函数f(x)=lnx-x+1,则f′(x)=1/x-1=(?)显然,当x∈(1,∞)时f′(x)<0;当x Looking at the questions in recent years, we can find that there are many kinds of comprehensive questions that frequently contain inequalities related to the natural logarithm lnx (or inverse function e ~ x) .This kind of questions is more difficult, intricate reasoning and complicated operation, Commonly afraid of the answer to feel thorny, and even lead to fear, resulting in very low score.First, we prove a simple inequality we all know: lnx≤x-1 Proof: Constructor f (x) = lnx-x +1 , F ’(x) = 1 / x-1 = (?) Obviously, f’ (x) <0 when x ∈