Adding a constant to predictors for Log transformation I have a dataset to predict customers' Churn that contains categorical and numeric variables. I intend to perform a Logistic regression. I want to apply log transformation to some of the numeric predictors by adding a constant so all the values are at least 1.
My questions are:
Does this constant have to be the same for all the variables intended to transform?
Does this procedure have an impact on the coefficient estimates?
How should I interpret this coefficient of the transformed variable?
Any references would be of great help :)

a. Why do you need using a transformation, and why manipulating the $log$ transformation? Try to think if there's any other way.
b. No, this constant doesn't have to be the same, but try to add one transformation at a time and check each time that you are really improving the model.
c. Of course coefficients will be affected. In logistic regression the output variable is $\hat{\pi}_i=P(y_i=1|x_i)$ but don't forget it is the sigmoid of $\hat{\theta}_i$:
$$\hat{\pi}_i=\frac{e^{\hat{\theta_i}}}{1+e^{\hat{\theta_i}}}=\frac{e^{\hat{\beta}^Tx_i}}{1+e^{\hat{\beta}^Tx_i}}$$
As you transform a variable, the corresponding coefficient is bound to change as the MLE solution still tries to optimize the solution with respect to $y_i$.
