Chapter 4 - Section 4.4 - Evaluating Logarithms and the Change-of-Base Theorem - 4.4 Exercises - Page 439: 105

$f(x)$ is obtained when $g(x)$ is translated $2$ units down.

Using properties of logarithm: $$f(x)=\ln\left(\frac {x}{e^2}\right)=\ln(x)-\ln(e^2)=\ln(x)-2\ln(e)=\ln(x)-2=g(x)-2$$ $f(x)$ is obtained when $g(x)$ is translated $2$ units down.