10: Here the decision which part to "put down" is a bit unusual. In a typical case we try to put down something that does not get too complicated in the process. In this example both logarithm and tangent become about equally bad when out down. Thus the decision stems from a secondary consideration: We want the part that we leave on top to improve, which will happen for logarithm. You should get
This is a fairly standard example of an indeterminate ratio, so use the l'Hospital rule.