Answer:
Step-by-step explanation:
An <em>inverse</em> 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.