Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.2 - Exponential Functions - Concept and Vocabulary Check - Page 463: 7


$(0, +\infty)$; $(-\infty, +\infty)$

Work Step by Step

RECALL: $y=\log_b{x} \longleftrightarrow b^y=x$, where $x \gt 0$, $b\gt 0$, and $b\ne 1$. Since $x \gt 0$, the domain of the logarithmic function is $(0, +\infty)$. There are no restrictions on $y$, so the range is the set of all real numbers, or $(-\infty, +\infty)$. Thus, the domain of the given function is $(0, +\infty)$, and the range is $(-\infty, +\infty)$.
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