Logarithm of sum

Asked Aug 24 '20 at 15:30

Active Aug 24 '20 at 15:30

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I have an equation of the form: $Y = A + A*e^{-b_1}+A*e^{-b_2}+A*e^{-b_3}+...+A*e^{-b_n}$.

I want to get rid of the exponential term. So, I am thinking of using a logarithm on both sides. It will help me to use geometric/arithmetic series for the summation of the $b_1, b_2, b_3,...,b_n$. Then I want to take antilog to get the original term. Can someone please help me to find the logarithm of the sum of the above equation? Thank you.

asked Aug 24 '20 at 15:30

Ajinkya Bankar

3

There aren't any nice transformations for the logarithm of a sum. – MasB Aug 24 '20 at 15:32
1

What is the unknown ? – Aug 24 '20 at 15:48
Is there any property of logarithm that we can use to simplify the logarithm of the sum as described in RHS of the above equation? – Ajinkya Bankar Aug 24 '20 at 16:02
You can write it as $\ln(A) + \ln(1+e^{-b_1} + ... + e^{-b_n})$. You cannot simplify further. – TheSilverDoe Aug 24 '20 at 18:58
Thank you for comments. I would appreciate if someone can provide more tricks. – Ajinkya Bankar Aug 25 '20 at 13:59

Logarithm of sum

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