  By building on a method introduced by Kashiwara and refined by Lichtin, we
give upper bounds for the roots of certain b-functions associated to a regular
function f in terms of a log resolution of singularities. As applications, we
recover with more elementary methods a result of Budur and Saito describing the
multiplier ideals of f in terms of the V-filtration of f and a result of the
second named author with Popa giving a lower bound for the minimal exponent of
f in terms of a log resolution.
