如何扩展和计算log(a + b)? [英] How to expand and compute log(a + b)?

问题描述

我想知道log(a + b)的完整扩展.

例如

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

与此类似，log(a + b)是否有扩展?

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

推荐答案

通常，不会扩展log(a + b)；您只需按原样处理它.就是说，在某些情况下，使用以下身份是有意义的:

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)

(实际上，在数学库中实现log时经常使用此标识).

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

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