Exercises 7880 develop an elegant approach to the exponential and logarithm functions
Chapter 5, Problem 80(choose chapter or problem)
Exercises 7880 develop an elegant approach to the exponential and logarithm functions. Define a function G(x) for x > 0: G(x) = x 1 1 t dt Defining bx Let b > 0 and let f (x) = F (xG(b)) with F as in Exercise 79. Use Exercise 78 (f) to prove that f (r) = br for every rational number r. This gives us a way of defining bx for irrational x, namely bx = f (x). With this definition, y = bx is a differentiable function of x (because F is differentiable).
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