## College Algebra (6th Edition)

We know that the logarithmic function of base $e$, or the natural logarithmic function, can be written as $f(x)=ln(x)$ or as $f(x)=log_{e}x$. Therefore, $ln(e^{7})=log_{e}e^{7}$. From the definition of the logarithmic function on page 456, we know that $b^{y}=x$ is equivalent to $y=log_{b}x$ (for $x\gt0$, $b\gt0$, and $b\ne1$). Therefore, $log_{e}e^{7}=7$, because $(e)^{7}=e^{7}$.