Re: how can I solve a transcendantale function?

• To: mathgroup at smc.vnet.net
• Subject: [mg48267] Re: how can I solve a transcendantale function?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Thu, 20 May 2004 04:03:43 -0400 (EDT)
• References: <c8f1df\$cvl\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```montgermont.aude at ec-lille.fr (aude) wrote:

> I can't solve this function:
>
> Log[1 - æ[t]] + (æ[t]/(1 - æ[t])) == 8*t
>
> I've tried with Sole, NSolve and Findroot without success.

Sometimes Mathematica isn't as bright as we'd like, and so we need to help
it a little.

True, Mathematica won't solve Log[1 - x] + (x/(1 - x)) == 8*t for x. But
let's replace 1-x by y. The equation can then be rewritten so that
Mathematica can solve it for y:

In[1]:= Solve[1 + y*Log[y] == (8*t + 1)*y, y]

```

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