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1-Newbie

## Symbolic solution to an exponential function

Hi All, I have a function which including two exponential components, whose power factor x and y are different. I was trying to solve it by hand or by Mathcad solver, but did not succeed. Would anyone give me the instruction how to do this?

Since an approximated solution is also acceptable, I  also tried to use the brute force method, in using match(0.9, XXX) and match(0.1, XXX) to solve, but it seems an exact match cannot be achieved. If someone can teach me how to get the approximated match, that would also be very helpful. Thank you!

1 ACCEPTED SOLUTION

Accepted Solutions
19-Tanzanite
(To:yhuang-3)

I don't think you will find a symbolic solution. To find a numeric solution you need to define a, b, c, x, and y. You can make the solve block a function of some or all of those parameters if you wish to vary them though.

9 REPLIES 9
19-Tanzanite
(To:yhuang-3)

I don't think you will find a symbolic solution. To find a numeric solution you need to define a, b, c, x, and y. You can make the solve block a function of some or all of those parameters if you wish to vary them though.

19-Tanzanite
(To:RichardJ)

A symbolic solution is possible for given values of x and y:

9-Granite
(To:RichardJ)

Hi Richard.

I think that this symbolic solution is only for the particular case that x=y.

Best regards.

Alvaro.

It appears you can often obtain a symbolic solution if you know the ratio between x and y:

However, for some ratios, the solution is too large to display:

9-Granite
(To:MJG)

Hi Mark.

But notice also that there are not a 'true' system of equations, both are independent and can be solved separately. This enable the use of root function.

Best regards.

Alvaro.

19-Tanzanite
(To:AlvaroDíaz)

Yes, you are right. It gets ugly otherwise:

9-Granite
(To:yhuang-3)

Hi Yhuang.

Symbolically, can't. Numerically, a solution in the attached.

Best regards.

Alvaro.

1-Newbie
(To:AlvaroDíaz)

Thank you Alvaro!

21-Topaz II
(To:yhuang-3)

Would not it be better to propose the problem in this way?

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