Four Powers in Order

★ 5/10functions calculus Monotonicity algebra Logarithms inequality

Problem

Let $0 < a < b < \dfrac{1}{\mathrm{e}}$ . Arrange

a^a, \quad b^b, \quad a^b, \quad b^a

in increasing order.

Answer

Solution

Difficulty	5/10
Topics	functions, calculus, Monotonicity, algebra, Logarithms, inequality

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