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.
College Algebra (11th Edition)
by Lial, Margaret L.; Hornsby John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
0321671791
ISBN 13:
978-0-32167-179-0
Chapter 4 - Section 4.4 - Evaluating Logarithms and the Change-of-Base Theorem - 4.4 Exercises - Page 439: 103
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