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Solving two simultaneous power equations.

Posted 10 years ago

I'm trying to solve two equations to provide coefficients for a power function based on two data points. I'd consider this trivial with pen and paper, but I don't understand why Mathematica won't find an answer. I figure it's operator error - any idea what I'm missing? Thanks in advance!

Power functions

POSTED BY: Walter Gurr
2 Replies
Posted 10 years ago

Ah, thank you - I wasn't aware of that option for Solve. I am using 8.0.1.0.

I noticed that MaxExtraConditions -> Automatic also gives a good solution. enter image description here

As a follow on question, is it possible for the Solve (or some another operator) to give 'a' as a function of 'b', even if not automatically? I often have to deal with problems such as this where one solution can be vastly simplified by substituting the expression of one of the other solutions. I tried hunting around but couldn't find an answer.

POSTED BY: Walter Gurr

I do not know how you obtained the above, since on V 10.02, it does not solve it as shown

Clear[y1, x1, y2, x2, a, b];
eq1 = y1 == a*x1^b;
eq2 = y2 == a*x2^b;
Solve[{eq1, eq2}, {a, b}]

gives

     Solve::nsmet: "This system cannot be solved with the methods available to Solve. 

But you can get the solutions use this:

Clear[y1, x1, y2, x2, a, b];
eq1 = y1 == a*x1^b;
eq2 = y2 == a*x2^b;
Solve[{eq1, eq2}, {a, b}, MaxExtraConditions -> All]

enter image description here

POSTED BY: Nasser M. Abbasi
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