In 3-5 sentences, describe the process for establishing the inverse of a logarithmic function and what will be the resulting function.

Answer 1

To establish the inverse of a logarithmic function, we start by setting the logarithmic function equal to a variable, typically \( y \). For example, for the function \( y = \log_b(x) \), where \( b \) is the base, we would rewrite this in exponential form: \( x = b^y \). Next, we swap the variables \( x \) and \( y \) to find the inverse, giving us \( y = b^x \). Thus, the resulting function is \( f^{-1}(x) = b^x \), which represents an exponential function.