I have a lin-log regression model like
$$Y = b_0 + b_1 \log(x_1 + 1) + e.$$
The distribution of $x_1$ is very skewed, thus I use the natural logarithm to get a more Gaussian like distribution. Because 3 out of 100 values have zero as entry I add a constant c, in my case plus 1, to avoid -Inf.
The resulting estimation of $b_1$ is about -0.14.
Without the constant the interpretation is clear: a 1% change in $x$ results in a $0.01\cdot b_1$ change in $y$.
I struggle with the constant. How can I account for it in my interpretation? If I change the value of c I get, of course, other estimates. I have chosen + 1 because this results in positive log values (the values of $x_1$ are originally positive too).
Or should I add a small value just to the three 0s?
Many thanks in advance and, please, a non mathematical answer ;-) Marco