※ 引述《pigheadthree (爬山)》之銘言：
: 題目：
: log_2 [log_3 (log_4 a)]-log_3 [log_4 (log_2 b)] = log_4 [log_2 (log_3 c)] = 0
: 答案：a + b + c = 89
: 小弟的想法，此題應該是要運用換底公式計算
: 舉例來講：log_10 c / [log_10 3 / (log_10 2 / log_10 4)] = 0
: 但是a、b、c未知，小弟卻無從假設數值計算，實在無從下筆！
: 麻煩版上前輩們不吝嗇指導，謝謝！
依照換底公式來講，小弟有個想法，但是答案卻差很多，所以不清楚是否正確？
log_4 [log_2 (log_3 c)] = log_10 c / [log_10 3 / (log_10 2 / log_10 4)] = 0
---> log_10 c / 2.63 = 0
---> log_10 c = 0
---> 10^0 = c = 1
log_2 [log_3 (log_4 a)]-log_3 [log_4 (log_2 b)] = 0
log_2 [log_3 (log_4 a)] = log_3 [log_4 (log_2 b)]
log_10 a / [log_10 4 / (log_10 3 / log_10 2)]
= log_10 b / [log_10 2 / (log_10 4 / log_10 3)]
log_10 a / 4.2 = log_10 b / 1.05
所以 log_10 a = 4.2 log_10 b = 1.05
10^4.2 = a = 15849
10^1.05 = b = 11.22
a+b+c = 15849 + 11.22 + 1 = 15861.22
麻煩版上前輩們不吝嗇指教，謝謝！
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※ 編輯: pigheadthree 來自: 1.165.189.17 (02/15 16:04)