Question

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, you start by expressing the logarithmic equation in its standard form, such as \( y = \log_b(x) \), where \( b \) is the base. To find the inverse, you swap the roles of \( x \) and \( y \), resulting in \( x = \log_b(y) \). Then, you exponentiate both sides using the base \( b \) to eliminate the logarithm: \( b^x = y \). The resulting function, which is the inverse of the original logarithmic function, is \( y = b^x \), representing an exponential function.