College Algebra (10th Edition)

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

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding: 9

Answer

false

Work Step by Step

RECALL: $\log_a{B^r} = r \cdot \log_a{B}$ The given expression is $\log_2{(3x^4)}=4\cdot\log_2{(3x)}$ Notice that the exponent $4$ in $(3x^4)$ applies only to $x$ but not to $3$. Thus, the rule above cannot be applied, which means that the exponent $4$ cannot be brought outside the logarithm. The rule above can only be applied if the given expression was $\log_2{(3x)^4}$. Thus, the given statement is false.
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