A2.7

recognize that the natural logarithmic function $f(x)={\log }_{e}x$, also written as $f(x)=\ln x$, is the inverse of the exponential function $f(x)=e^x$, and make connections between $f(x)=\ln x$ and $f(x)=e^x$ [e.g., $f(x)=\ln x$ reverses what $f(x)=e^x$ does; their graphs are reflections of each other in the line $y=x$; the composition of the two functions, $e^{\ln x}$ or $\ln e^x$, maps $x$ onto itself, that is, $e^{\ln x}=x$ and $\ln e^x=x$]