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MathGroup Archive 1996

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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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