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

Question

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

Answer 1

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