Suppose we have a variety $X$ over a field of characteristic zero. Choose any ideal sheaf $\mathcal{I}$ on $X$. Is every log resolution of the pair $(X,\mathcal{I})$ a sequence of blow ups?

Suppose we have a variety $X$ over a field of characteristic zero. Choose any ideal sheaf $\mathcal{I}$ on $X$. Is every log resolution of the pair $(X,\mathcal{I})$ a sequence of blow ups? I cannot find a reference for such a fact, if at all true, nor is there a counterexample in mind. Any help with be appreciated!