Question

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 1

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).