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標題: [Core] 有冇人識呢條 log [打印本頁]

作者: A380123    時間: 2020-12-16 11:04 AM     標題: 有冇人識呢條 log

見下圖, find for possible x, y, p and q
(答案有 x=3, y=2, p=8, q=9 or x=5, y=5, p=32, q=25)

可以點solve?
[attach]53494[/attach]
作者: blazehaze    時間: 2020-12-17 05:46 AM

let say we have a real number k such that log_x(log_y(p)) = log_y(log_x(q)) = k
then we obtain p = y^(x^k) and q = x^(y^k)
hence the solution set is {x, y, y^(x^k), x^(y^k) : x > 0, x ≠ 1, y > 0, y ≠ 1, k ∈ R}
作者: A380123    時間: 2020-12-17 02:26 PM     標題: 回覆 2# blazehaze 的帖子

神啊!! 太強了!!





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