2. In class, we have defined In(r) and et. The purpose of this exercise is to define logarithms and exponentials for any base a > 0. You will not need to know the content of this exercise for the midterm, but it is still important material. For any real number a > 0 we define at = ex In(a) 1 and loga (T) = In(a) In(r). Use these definitions to solve the following questions: (a) Show that In(at) = r In(a). (b) Show that d r _ In(a) . at. dx (c) Show that log (at ) = I. (d) Show that loga (T) = I. (c) Show that d 10ga (T) = In(a)