Re: Solving simple equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg122713] Re: Solving simple equations*From*: Mathieu <mathtd at gmail.com>*Date*: Mon, 7 Nov 2011 05:52:55 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111050949.EAA10511@smc.vnet.net> <j95p1m$m34$1@smc.vnet.net>

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

**References**:**Solving simple equations***From:*Mathieu <mathtd@gmail.com>