Subject: Best way to solve equations with logarithms?
From: Jaime E. Villate
Date: Fri, 10 Oct 2003 09:28:04 +0100
On Thu, Oct 09, 2003 at 03:02:49PM -0400, Stavros Macrakis wrote:
> As the Emacs bug reporting guidelines say, "The most important principle
> in reporting a bug is to report _facts_. Hypotheses and verbal
> descriptions are no substitute for the detailed raw data."
You're right; it even takes less time to copy and paste from an actual
Maxima sesssion :-)
> Your hypothesis was that the problem had to do with "simple equations
> involving logarithms", but in fact, the problem has to do with the
> power; the same problem appears with:
>
> solve((x+1)^5/x^5=y,x)
now I see the problem; thanks for your explanation. It would be nice
if Maxima tried first taking roots, (x+1)/x=y^(1/5), rather than expanding
powers. Or solve could try both approaches and see which one leads to
x=f(y).
> which gives 5 solutions of the form f(x)= rootunity * y^(1/5). I
> daresay Maxima could present solutions like this in a more compact form,
> using something like %E^(2*%n1*%i*%pi/5), where %n1 ranges over the
> integers, just as %r1 ranges over the reals. SMOP/TBD: Small matter of
> programming, to be done.
Nice idea. I wish I knew more Lisp to understand what would have to be done.
> The trick in your original problem is to prevent the 35 from moving into
> the log. Logcontract only moves integral factors, so if you substitute
> q for 35, and then logcontract, things will go much more smoothly
Sure, but that relies on human intervention; how could a script be
written to discover such common factors and substitute them for a symbol?
Regards,
Jaime