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Answer to Question #15119 in Calculus for hsd

Question #15119
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?
Expert's answer
y=bx,so x=logb⁡y using the formula for logarithm logb⁡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).

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