Re: question on log transformation
- From: Richard Ulrich <Rich.Ulrich@xxxxxxxxxxx>
- Date: Tue, 14 Feb 2006 18:58:16 -0500
On 13 Feb 2006 09:33:49 -0800, "HJW" <hjw48823@xxxxxxxxx> wrote:
Dear listers,
Suppose x* maximizes the function f(x) - g(x). Does the same x* also
maximize ln(f(x)) - ln(g(x))? I know it generally does not, but how to
proof it? What if f(x) and g(x) are both positive by definition? Any
suggestion will be appreciated.
You can re-write ln(f) -ln(g) as ln(f/g), which is maximized
when f/g is maximum.
f/g is not necessarily monotonic (or in the right direction, even)
with (f-g).
--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.
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