Answer
$f(x)$ is obtained when $g(x)$ is translated $2$ units up.
Work Step by Step
Using properties of logarithm:
$$f(x)=\ln(e^2x)=\ln(e^2)+\ln(x)=2\ln(e)+\ln(x)=2+\ln(x)=2+g(x)$$
$f(x)$ is obtained when $g(x)$ is translated $2$ units up.
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