Multi-Logarithms (Posted on 2004-12-08)

	Submitted by SilverKnight
Rating: 3.4000 (5 votes)
Solution:	(Hide)
Let: a = log9(x) = log12(y) = log16(x+y) Then, 16^a = x + y = 9^a + 12^a. Completing the square, we get: (3^a + 1/2(4^a))^2 = (5/4)(4^a)^2. Therefore 3^a = (√5-1)/2)4^a. Then y/x = 12^a/9^a = 4^a/3^a = 2/(√5-1) = (1+√5)/2

	Subject	Author	Date
	Puzzle Solution (Method III)	K Sengupta	2008-04-06 13:10:28
	Puzzle Solution (Method II)	K Sengupta	2008-02-28 05:39:49
	Puzzle Solution	K Sengupta	2007-03-19 12:01:53
	re(3): I think	Richard	2005-01-21 03:11:36
	re(2): I think	matt	2005-01-20 23:39:39
	re: I think	Charlie	2005-01-20 19:17:40
	I think	matt	2005-01-20 17:01:13
	re: Generalization	Jer	2004-12-09 17:31:15
	Generalization	owl	2004-12-09 17:07:29
	solution	Charlie	2004-12-08 15:29:24