Re: Solving simple equations

• To: mathgroup at smc.vnet.net
• Subject: [mg122723] Re: Solving simple equations
• From: Dana DeLouis <dana01 at me.com>
• Date: Mon, 7 Nov 2011 05:54:43 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```>  ...Reduce (& Solve) doesn't work...
>  ...Solve[(A*n^a)^b/n == c, n]

Hi.  The only way I found to get a real solution for this particular problem is to use PowerExpand:

data = {A -> 2, a -> 3, b -> 4, c -> 5.};

equ = PowerExpand[(A*n^a)^b/n == c] ;

Solve[equ, n]

Which gives:

n -> (c/A^b) ^ (1/(a*b - 1))

% /. data
0.8996576447849666

Check with Solve using the same data...

(A*n^a)^b/n == c   /. data

16*n^11 == 5.

NSolve[%, n, Reals]

n -> 0.8996576447849665

= = = = = = = = = =
HTH
Dana DeLouis
= = = = = = = = = =

On Nov 5, 4:57 am, Mathieu <mat... at gmail.com> 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

```

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