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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