# Solve simple logarithmic question

1. Sep 30, 2008

### preet

1. The problem statement, all variables and given/known data
Ae^dt + Be^ft + Ce^gt + De^ht + ... = Y

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

2. Relevant equations

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

3. 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

2. Sep 30, 2008

There is no way to simplify

$$\ln \left(A e^{at} + Be^{bt} + \dots + \right)$$

It is impossible to simplify the logarithm of a sum.

3. Sep 30, 2008

### 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 et, try to solve for et, and then take the logarithm.