logarithm of a sum or addition I search a

Landen Barber

Landen Barber

Answered question

2022-03-23

logarithm of a sum or addition
I search a general rule for calculating the logarithm of a sum or addition. I know that
ln(a+b)=ln(a(1+ba))=ln(a)+ln(1+ba)
but when the sum implies more terms, how to generalize its calculation/computation? For example when
ln(a+b+c)
or when
ln(iai)
like when we have to compute the denominator of a Bayes formula using log-likelihoods? Thanks for your incoming help.

Answer & Explanation

undodaonePvopxl24

undodaonePvopxl24

Beginner2022-03-24Added 13 answers

Same thing you can do with more than three terms
ln(a+b+c)=ln((a+b)(1+ca+b))=
=ln(a+b)+ln(1+ca+b)=
=ln(a(1+ba))+ln(1+ca+b)=
=lna+ln(1+ba)+ln(1+ca+b)

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