Question

证明下列不等式,设b>a>e,则a^b>b^a

Answer 1

设b>a>e

a^b ＞ a^a

又 a^a ÷ b^a=（a/b）^a

a/b ＜1,a＞e

可得a^a ÷ b^a=（a/b）^a＜1

即a^a ＞b^a

a^b>b^a