       Re: FindRoot with Logarithmic terms

• To: mathgroup at smc.vnet.net
• Subject: [mg116028] Re: FindRoot with Logarithmic terms
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Sat, 29 Jan 2011 05:29:21 -0500 (EST)
• References: <ihu8is\$1pj\$1@smc.vnet.net>

```skunkwerk wrote:

> Hi,
>   I'm trying to find the roots of a logarithmic equation that I've plotted successfully (I can see both roots are between 0 and 1).
>
> expr = 7500*x*(1 - x) + 325*8.314*(x*Log[x] + (1 - x)*Log[(1 - x)])
> FindRoot[expr == 0, {x, 0, 1}]
>
> FindRoot:nlnum: the function value(indeterminate) is not a list of numbers with dimensions {1} at {x} = {0.}
>
> any ideas?
>
> thanks
>

Your expr is indeterminate at x=0 and x=1 due to the Log. So you have
the following possibilities:

1. Adjust the search interval of FindRoot:

FindRoot[expr == 0, {x, 0.2, 0.5}] ----> {x->0.468458}
FindRoot[expr == 0, {x, 0.5, 0.9}] ----> {x->0.531542}

2. Use Reduce:

Reduce[expr==0,x,Reals] ----> x=0.468458 || x=0.513542

you will get a message about inexact coefficients though. If you use
Reduce[Rationalize[expr]==0,x,Reals] you will get two solutions in the
form of Root[]-objects.

//Peter

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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