1. Use the fact that loga: is the inverse function of e": and the denition of 230' to show that for a real and a: > 0, log($a) : a log 3:. 2. Suppose f (as) is a positive real valued function and that log f (as) is differentiable at 2:. Show that f (:17) is differentiable at x and that Hint: To show that f (:17) is differentiable, you can write it as the composition of two differentiable functions and apply the chain rule. 3. Use problems 1 and 2 to show that f(a:) : as" is differentiable for a," > 0 and a real with f'(:1:): Cilia1