# Intercept term in logistic regression

Suppose we have the following logistic regression model:

Is $\beta_0$ the odds of the event when $x_1 = 0$ and $x_2=0$? In other words, it is the odds of the event when $x_1$ and $x_2$ are at the lowest levels (even if this is not 0)? For example, if $x_1$ and $x_2$ take only the values $2$ and $3$ then we cannot set them to 0.

$\beta_0$ is not the odds of the event when $x_1 = x_2 = 0$, it is the log of the odds. In addition, it is the log odds only when $x_1 = x_2 = 0$, not when they are at their lowest non-zero values.