In 3–5 sentences, describe the process for establishing the inverse of a logarithmic function and what will be the resulting function.(4 points)

Answer 1

To establish the inverse of a logarithmic function, start with the logarithmic equation \( y = \log_b(x) \), where \( b \) is the base of the logarithm. To find the inverse, switch the roles of \( x \) and \( y \), yielding \( x = \log_b(y) \). Next, exponentiate both sides with base \( b \) to eliminate the logarithm, resulting in \( y = b^x \). Therefore, the inverse of the logarithmic function \( y = \log_b(x) \) is the exponential function \( y = b^x \).