Let X be a nonsingular complex projective variety and D a locally quasi-homogeneous free divisor in X. We ask if the formula c_{SM}(1_X )- c_{SM}(1_D)=c(\textup{Der}_X(-\log D))\cap [X] is true in this situation. In the presentation I will strive to convey the following information: 1. What is the logarithmic comparison theorem? 2. How is the logarithmic comparison theorem related to the proposed formula? 3. A sketch of an argument which covers the numerical aspect of the formula.