Can I add a constant and then transform my explanatory variable? [duplicate]

My current model is of the form $$\log(\frac{y_i}{1-y_i}) = \beta_0 + \beta_1 x_1+\beta_2 x_2.$$ Is it okay if I consider the model $$\log(\frac{y_i}{1-y_i}) = \beta_0 + \beta_1 x_1+\beta_2 \log(x_2+1),$$ where $$x_2$$ is continuous?

$$x_2$$ can take the value 0 hence why I am adding the constant 1. I am also applying the log transformation due to interpretability.