Solve simple logarithmic question

[preet]

Homework Statement

Ae^dt + Be^ft + Ce^gt + De^ht + ... = Y

Where A-Y and d,f,g,h, etc are constants.

Homework Equations

Logarithmic identities... ( log(AB) = log(A) + log(B), log(A^x) = x log A, etc)

The Attempt at a Solution

I could do this if there was only one term on the left side of the equation. I don't know how to simplify the left hand terms... ie. to solve I would have taken ln( left hand side ) = ln (Y) but I don't know how to deal with the multiple terms on the left side... specifically I don't know what to do with ln ( Ae^at + Be^bt + Ce^ct) and so on.


Thanks,

-Preetj

 

[statdad]

There is no way to simplify

<br /> \ln \left(A e^{at} + Be^{bt} + \dots + \right)<br />

It is impossible to simplify the logarithm of a sum.

 

[HallsofIvy]

What reason do you have to think that there is an exact algebraic solution to this equation? IF d, f, g, h are integers, then you could write this as a polynomial equation for e^t, try to solve for e^t, and then take the logarithm.