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Re: Solving simple equations


On Nov 6, 5:54 am, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote:
> This may be a "very simple equation" for a human but not for a computer
> program. First, it can only be solved by making additional assumptions
> (of the kind you tried to use). However, first of all Solve (and Reduce)
> cannot receive assumptions through the Assumptions mechanism so your
> Assuming is doing nothing at all.  Second, there is no general algorith=
m
> that can solve transcendental equations of this kind even when all these
> assumptions are satisfied. The fact that this particular equation can be
> easily solved is due to it being a very special case of an unsolvable
> general type. So, in such situations, you usually have to intervene and
> simplify it to a form that Solve can recognise. In this particular case,
> you can take Logs of both sides, PowerExpand (which works under your
> assumptions) and the rest Solve can do for you.
>
> n /. Solve[PowerExpand[Log[(A*n^a)^b/n] == Log[c], Assumptions ->
>       {A > 0, n > 0, a > 0, b > 0}], n][[1]]
>
> E^((Log[c] - b*Log[A])/(a*b - 1))
>
> (Note that if you change your equation even slightly, e.g. Log[(A (n +
> 1)^a)^b/n] == Log[c], it will become unsolvable).
>
> Andrzej Kozlowski
>
> On 5 Nov 2011, at 10:49, Mathieu wrote:
>
>
>
>
>
>
>
> > Mathematica seems to struggle with very simple equations:
>
> > Solve[(A*n^a)^b/n == c, n]
> > Solve::nsmet: This system cannot be solved with the methods available
> > to Solve
>
> > Reduce doesn't work either. Even if I add assumptions:
> > Assuming[A > 0 && 1 > a > 0 && 1 > b > 0 && c > 0 && n > 0, Solve[(A
> > n^a)^b/n == c, n]]
> > Solve::nsmet: This system cannot be solved with the methods available
> > to Solve. >>
>
> > Is there a way for Mathematica to solve these equations?
>
> > Many thanks,
> > Mathieu

Thanks for the reply. That is quite useful.

Mathieu



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