我要被这题弄疯掉了 我要被这题弄疯掉了 x^x*y^y=z^z x=12^6 y=6^8 求z
6个回答

x log x + y log y = z log z

z log z =

12^6 * 6 log 12 + 6^8 * 8 log 6 =

12^6 * 6 (log 3 + 2 log 2) + 6^8 * 8 ( log 2 + log 3) =

(12^6 * 6 + 6^8 * 8) log 3 + (12^7 + 6^8 * 8) log 2 =

(3^7 * 2^13 + 2^11 * 3^8) log 3 + (2^14 * 3^7 + 2^11 * 3^8) log 2 =

(3^7 * 2^11) [ ( 4+ 3) log 3 + (8+ 3) log 2)] =

(3^7 * 2^11) log (3^7 * 2^11)

thus,

z = 3^7 * 2^11

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