How to expand and compute log(a + b)?

math logarithm
Aditya Singh picture Aditya Singh · Oct 20, 2010 · Viewed 244.1k times · Source

I would like to know the complete expansion of log(a + b).

For example

log(a * b) = log(a) + log(b);
log(a / b) = log(a) - log(b);

Similar to this, is there any expansion for log(a + b)?

Answer

Stephen Canon picture Stephen Canon · Oct 20, 2010

In general, one doesn't expand out log(a + b); you just deal with it as is. That said, there are occasionally circumstances where it makes sense to use the following identity:

log(a + b) = log(a * (1 + b/a)) = log a + log(1 + b/a)

(In fact, this identity is often used when implementing log in math libraries).

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