| Author |
Comment/Response |
Oleg Urminsky
|
 03/08/02 1:57pm
I am trying to solve several systems of equations with exponential parameters. The problem is that some of them can be solved with a Log transform, but neither Solve or Reduce finds those solutions.
As an example:
In[482]:=
Solve [{ d1==k*x1^s, d2==k*x2^s}, {k, s}]
Out[482]=
{}
No solution is found. I know, however, that there is a solution if you take the Log of both sides:
In[483]:=
Solve [{ Log[d1]==Log[k*x1^s],Log[d2]==Log[k*x2^s]}, {k, s}])
Out[483]=
{}
It still finds no solution. The only way I could get it to work was to use PowerExpand:
In[484]:=
Solve[{ Log[d1]==PowerExpand[Log[k*x1^s]],
Log[d2]==PowerExpand[Log[k*x2^s]]}, {k, s}]
Out[484]=
s=(-Log[d1] + Log[d2])/(-Log[x1] + Log[x2]),
k=[ExponentialE]^\(\(Log[d2]\ Log[x1] - Log[d1]\ \
Log[x2]\)\/\(Log[x1] - Log[x2]\)\)}}\)
I had the same problem with Reduce.
Here's my question. Is there another routine I could use that will attempt log transforms in searching for a solution? Or would it make a difference if I restricted values to the reals, and can I do that in Solve or Reduce?
I can of course try each equation both ways: directly and forcing the log transform, but I wanted to know if there was a better way.
Thanks,
Oleg
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