College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding - Page 449: 39


$x \gt 3$ or $(3, +\infty)$

Work Step by Step

RECALL: The logarithmic function $f(x) = \ln{x}$ is defined only when $x \gt 0$. Thus, its domain is $x \gt 0$. This means that the function $f(x) = \ln{(x-3)}$ is defined only when $x-3 \gt 0$. Solve the inequality to obtain: $x-3 \gt 0 \\x-3+3 \gt 0+3 \\x \gt 3$ Thus, the domain of the given function is $x \gt 3$. In interval notation, the domain is $(3, +\infty)$.
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