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Solve simple logarithmic question

  1. Sep 30, 2008 #1
    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. jcsd
  3. Sep 30, 2008 #2

    statdad

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    Homework Helper

    There is no way to simplify

    [tex]
    \ln \left(A e^{at} + Be^{bt} + \dots + \right)
    [/tex]

    It is impossible to simplify the logarithm of a sum.
     
  4. Sep 30, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    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.
     
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