2006-03-02T05:35:24ZFluxBBhttp://www.mathisfunforum.com/viewtopic.php?id=2904Rimiq please, help us more.]]>http://www.mathisfunforum.com/profile.php?id=21282006-03-02T05:35:24Zhttp://www.mathisfunforum.com/viewtopic.php?pid=29544#p29544We must prove that log(nu+(1-n)v)>=nlog(u)+(1-n)log(v) Is there some unequation for log(a+b) and log(a)+log(b)?]]>http://www.mathisfunforum.com/profile.php?id=21282006-03-01T07:00:37Zhttp://www.mathisfunforum.com/viewtopic.php?pid=29368#p29368I guess I can give you some hints about the solution...you can consider the fact that log is a concave function.]]>http://www.mathisfunforum.com/profile.php?id=29902006-03-01T05:35:07Zhttp://www.mathisfunforum.com/viewtopic.php?pid=29356#p29356No mathsy thats not quite a proof...but I can give you hints if you want...this is simple...indeed]]>http://www.mathisfunforum.com/profile.php?id=29902006-02-25T05:28:07Zhttp://www.mathisfunforum.com/viewtopic.php?pid=28772#p28772If n = 0, then the inequality simplifies down to v ≤ v.
Similarly, if n = 1, then the inequality simplifies down to u ≤ u.
So u[sup]n[/sup] x v[sup]1-n[/sup] ≤ nu+(1-n)v all the time because they are actually always equal to each other.
]]>http://www.mathisfunforum.com/profile.php?id=6412006-02-23T16:51:50Zhttp://www.mathisfunforum.com/viewtopic.php?pid=28562#p28562Hence, the question would be..... Prove that u[sup]n[/sup] x v[sup]1-n[/sup]≤nu+(1-n)v where n∈(o,1) and u,v > 0]]>http://www.mathisfunforum.com/profile.php?id=6822006-02-23T08:32:17Zhttp://www.mathisfunforum.com/viewtopic.php?pid=28519#p28519To do superscripts:
u[sup]n[/sup]
and you get: u[sup]n[/sup]
]]>http://www.mathisfunforum.com/profile.php?id=22006-02-23T08:07:09Zhttp://www.mathisfunforum.com/viewtopic.php?pid=28517#p28517prove that , u (to the power)n × v(to the power)(1-n) ≤nu + (1-n)v n∈(o,1) and u,v > 0 by the way how do I bring this superscripts ? As word files are not working.]]>http://www.mathisfunforum.com/profile.php?id=29902006-02-23T05:56:28Zhttp://www.mathisfunforum.com/viewtopic.php?pid=28505#p28505