Presuming b >= 0, then log(a+b*x^2) is convex for b*x^2 <= a and concave for b*x^2 >= a. Therefore it is neither convex nor concave (over the entirety of its natural domain), unless a = 0 or b = 0.
Presuming b >= 0, then log(a+b*x^2) is convex for b*x^2 <= a and concave for b*x^2 >= a. Therefore it is neither convex nor concave (over the entirety of its natural domain), unless a = 0 or b = 0.