What is the inverse of f(x)=e^x

Step-by-step explanation:

An inverse function is any function that "undoes" another function. If we think of the function as some kind of machine that takes in a number as input and produces a number as an output, when we give inverse function the number as in input, we get , our original input, as the output

We need a function that undoes , and the natural choice for undoing an exponent is with a logarithm. Here, our base is , so we'll choose as our inverse function. Let's see how that works:

is the power we have to raise to to get , which is , so

And we have our function.

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