[Tips] Compare x ^ y and y ^ x size of

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First Japanese sentence X $ $ $ or $ Y $ 0 and $ $ $ y = -1 in the case.

For the remaining normal circumstances, apparently logarithmic power can be converted to a multiplier.

That is to take $ x ^ y $ $ \ $ into LN $ y \ ln {x} $, $ y ^ x $ take $ \ $ into LN $ x \ ln {y} $

Then $ x ^ y $ and $ y ^ x $ equal magnitude relation $ y \ ln {x} $ and $ x \ ln {y} $ magnitude relationship

Transposition may be equal to $ \ frac {\ ln {x}} {x} $ and $ \ frac {\ ln {y}} {y} $ magnitude relationship

Obviously when $ x, y \ ge 1 $, the