\begin{frame} \frametitle{1st Midterm Exam - Review} \begin{exampleblock}{} Find the inverse function of \begin{talign} f(x) = \frac{1+\log x}{2\log x + 5} \end{talign} \pause We have \begin{talign} y = \frac{1+\log x}{2\log x + 5} &\mpause[1]{\implies y\cdot (2\log x + 5) = 1+\log x} \\ &\mpause[2]{\implies 2y\log x + 5y = 1+ \log x} \\ &\mpause[3]{\implies 2y\log x -\log x = 1-5y } \\ &\mpause[4]{\implies \log x \cdot (2y - 1) = 1-5y } \\ &\mpause[5]{\implies \log x = \frac{1-5y}{2y - 1} } \\ &\mpause[6]{\implies x = 10^{\frac{1-5y}{2y - 1}} } \end{talign} \pause[9] Thus the inverse function is $f(y) = 10^{\frac{1-5y}{2y - 1}}$. \end{exampleblock} \end{frame}