Answer to Question #15119 in Calculus for hsd

Question

Let b > 0 and b≠1. We consider the function f(x) = b^x with domain D = lR. Determine the inverse function f^-1(y) write it in terms of the natural logarithm ln y, and specify its domain. What happens if b = 1?

Answer 1

y=b^x,so x=log_b⁡y using the formula for logarithm log_b⁡y=ln⁡y/ln⁡b
And so x=ln⁡y/ln⁡b . If b=0 inverse function won’t exist because to any values of x corresponds the only one y (it’s 1).