Separating the log of a sumI know there is no formula to separate the log...

independanteng

independanteng

Answered

2022-10-31

Separating the log of a sum
I know there is no formula to separate the log of a sum, e.g. log ( X + Y ) into two parts, but are there any approximation rules that can allow me to achieve this objective?
E t ( 1 + r t + 1 K ) = E t [ 1 X t + 1 α A 0 Y t + 1 K t + 1 + Q t + 1 ( 1 δ ) Q t ]
Suppose we ignore the expectations operator for the moment.

Answer & Explanation

megagoalai

megagoalai

Expert

2022-11-01Added 22 answers

log ( X + Y ) = log ( X ) + log ( 1 + Y / X ), so if either X is small compared to Y or vice versa then you can approximate with a Taylor approximation.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?