These are approximations, which, I guess, only apply for small growth rates $g$ ($g$ is a function that denotes the change in its argument).
$$\begin{align}
g(xy) &= g(x) + g(y) \\
g(x/y) &= g(x) − g(y) \\
g(x^\alpha) &= \alpha g(x)
\end{align}$$

And there are also these rules

$$\dfrac{\Delta(x\*y)}{xy} = \dfrac{\Delta x}x + \dfrac{\Delta y}y$$

and 

$$\dfrac{\Delta(x^\alpha)}{x^\alpha} = z\*\dfrac{\Delta x}x$$

I guess $g(x)$ equals $\dfrac{\Delta x}x$? So these rules are actually the same as the above ones.

However, I don't see how this can be derived from a log growth equation (which one?). I know a natural log function of a percentage change (e.g. $1.02$) approximates a percentage change that represents growth rates very close to zero (e.g. $0.02$), but ...

Thank you

babi