Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.4 Logarithms, #75 · Calculus · Differentiation rules

Find a pair of positive integers for which

Find a pair of positive integers for which $x^{y} = y^{x}$ . Show how to change this equation to $(ln x) / x = (ln y) / y$ . So look for two points at the same height in Figure 6.13. Prove that you have discovered all the integer solutions.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.4 Logarithms, #75

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