Why log(A) can be seen as %ΔA in economics? We usually see deduce in economitrics changes $lnY$ to $\%\Delta Y$, say we have Cobb-Douglas function like this $Y=AK^αL^{1−α}$, in one of the book I read, it is changed to :

But why can we do like this ?

This may help:
$$
\Delta Y\simeq \Delta A (K^\alpha L^{1-\alpha})+\Delta K (A\alpha K^{\alpha-1}L) + \Delta L (A (1-\alpha) L^{-\alpha})
$$
is just the total differential of $Y=Y(A,K,L)$. Then divide everything by $Y=A K^\alpha L^{1-\alpha}$ and you get the equation.
(Another option how to look at this equation is to concider the quantity $\Delta f/f$ to be $\Delta (\ln f)$ and apply $\Delta$ to $\ln Y=\ln A + \alpha\ln K + (1-\alpha)\ln L$.)
