I'm reading a paper where they use a discrete approximation of a logarithmic mass growth rate as follows:
$$ \frac{d \log M}{d \log t} \approx \frac{(t_B + t_A)(M_B - M_A)}{(t_B - t_A)(M_B + M_A)}$$
I'm trying to derive this approximation, but wasn't successful thus far. I tried forward, centered and backward differencing, using Taylor expansions and $\log(x) \approx (x-1) - \frac{(x-1)^2}{2} + ...$ for $x \rightarrow 1$, but haven't gotten that result. In particular, I don't see how the factors $(M_A + M_B)$ and $(t_A + t_B)$ come into play.
Can anyone help me out?