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=b^{x},so x=log_{b}y using the formula for logarithm log_{b}y=lny/lnb

And so x=lny/lnb . If b=0 inverse function won’t exist because to any values of x corresponds the only one y (it’s 1).

And so x=lny/lnb . 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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