Question

Which function is the inverse of F(x) = bx?

Answer 1

The inverse of the function f(x) = bˣ is the logarithmic function with base b, denoted as
`f(y) = log_b(y).`

The inverse of the function f(x) = is the logarithmic function with base b, denoted as
`f(x) = log_b(x)`. This means that for any value y, f(y) is the value x such that f(x) = y. In other words, if f(x) = , then f(y) = x when = y.

To see why this is true, consider the following equation:

= y

Taking the logarithm of both sides with base b, we get:

`log_b() = log_b(y)`

Since
`log_b()` = x, we have:

`x = log_b(y)`

Therefore, f(y) =
`log_b(y).`