Log of a sum with three terms

From other posts on here I learned that the following is true:

$$\log(a + b) = \log\left(a \cdot \left(1 + \frac{b}{a}\right)\right) = \log(a) + \log\left(1 + \frac{b}{a}\right)$$

What about $\log(a + b + c)$?

• $log(a+b+c)=log((a+b)+c)$ – ModOverRing May 1 '17 at 11:28

$$\log((a+b)+c)=\log\left((a+b)\cdot\left(1+\frac{c}{a+b}\right)\right)$$ $$=\log(a)+ \log\left(1+\frac{b}{a}\right)+\log\left(1+\frac{c}{a+b}\right)$$