To establish the inverse of a logarithmic function, such as \( f(x) = \log_b(x) \), we start by rewriting the function in exponential form. We set \( y = \log_b(x) \), which implies that \( b^y = x \). To find the inverse, we then solve for \( x \) in terms of \( y \), yielding \( x = b^y \). Thus, the inverse function is \( f^{-1}(x) = b^x \), which transforms the logarithmic function into an exponential function.
In 3–5 sentences, describe the process for establishing the inverse of a logarithmic function and what will be the resulting function.
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