Modeling rare events in logistic regression



I am pasting the blog link which I am referring to !

In order to offset the initial bias sampling for rare events, it has been used “{- Log odds (actual)} = slope * {-Log odds(predicted)} + Intercept” for correction at the end of logistic fit. (deciles table)
it is like LOG (base 10) rather than natural log (LN). What is the reason behind using
LOG10 ? if we use this, will it sync up to overall modeling ? I mean LN
(Odds) = B0+B1 *X is our theme for Logistic regression ?
Looking forward for your reply, btw.