Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Re: [mg4782] Help - transposing equation
Replies: 0

 Andrei Constantinescu Posts: 32 Registered: 12/7/04
Re: [mg4782] Help - transposing equation
Posted: Sep 20, 1996 12:50 AM

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