Re: Help - transposing equation
- To: mathgroup at smc.vnet.net
- Subject: [mg4823] Re: [mg4782] Help - transposing equation
- From: Andrei Constantinescu <constant at athena.polytechnique.fr>
- Date: Fri, 20 Sep 1996 01:12:43 -0400
- Sender: owner-wri-mathgroup at wolfram.com
The equations are pretty complicated as you have a DegK and Log[DegK]
in the same time, so generally will have just a numerical solution.
However there are some manipulations on mathematica that can transform everything in one
equation:
443.414 Log[10]
Out[4]= -5.427146 + 3.65297 x - ------- == -------
y Log[a]
Log[b]
In[3]:= %1 /. Log[DegK] -> x
443.414 Log[10]
Out[3]= -5.427146 - ------- + 3.65297 x == -------
DegK Log[a]
In[4]:= % /. DegK -> y
443.414 Log[10]
Out[4]= -5.427146 + 3.65297 x - ------- == -------
y Log[a]
In[5]:= %2 /. Log[DegK] -> x
2 Log[10]
Out[5]= -36.74404 + 24.10071 x - 3.38936 x == -------
Log[b]
In[6]:= Solve[ % , x ]
-6 6
Out[6]= {{x -> (1.4752 10 (2.41007 10 Log[b] -
12 2
> 1. Sqrt[5.80844 10 Log[b] -
6 6
> 1.35574 10 Log[b] (230259. + 3.6744 10 Log[b])])) / Log[b]},
-6 6
> {x -> (1.4752 10 (2.41007 10 Log[b] +
12 2
> Sqrt[5.80844 10 Log[b] -
6 6
> 1.35574 10 Log[b] (230259. + 3.6744 10 Log[b])])) / Log[b]}}
In[7]:= Solve[ %4 , y ]
0 Log[b] -
6 6
> 1.35574 10 Log[b] (230259. + 3.6744 10 Log[b])])) / Log[b]}}
In[7]:= Solve[ %4 , y ]
Out[7]= {{y -> ----------------------------------------}}
-0.630332 - 1.48568 Log[a] + 1. x Log[a]
In[8]:= % /. %6
Out[8]= {{{y ->
> (121.385 Log[a]) /
> (-0.630332 - 1.48568 Log[a] +
-6 6
> (1.4752 10 Log[a] (2.41007 10 Log[b] -
12 2
> 1. Sqrt[5.80844 10 Log[b] -
6 6
> 1.35574 10 Log[b] (230259. + 3.6744 10 Log[b])])) /
> Log[b])}}, {{y ->
> (121.385 Log[a]) /
> (-0.630332 - 1.48568 Log[a] +
> Log[b])}}, {{y ->
> (121.385 Log[a]) /
> (-0.630332 - 1.48568 Log[a] +
-6 6
> (1.4752 10 Log[a] (2.41007 10 Log[b] +
12 2
> Sqrt[5.80844 10 Log[b] -
6 6
> 1.35574 10 Log[b] (230259. + 3.6744 10 Log[b])])) / Log[b]
> )}}}
.... and now you have actually y = DegK as a function of Log[DegK] = x , which
gives you the desired equation in DegK !
Regards,
a + andrei
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