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: 38

Answer

$\log_3{x} - 2$

Work Step by Step

RECALL: (1) $\log_a{(MN)} = \log_a{M} + \log_a{N}$ (2) $\log_a{\left(\dfrac{M}{N}\right)} = \log_a{M} - \log_a{N}$ (3) $\log_a{a} = 1$ Note that $9=3(3)$. So the given expression is equivalent to: $\log_3{\left(\dfrac{x}{3\cdot3}\right)}$ Using rule (2) above, the given expression is equivalent to: $=\log_3{x} - \log_3{(3 \cdot 3)}$ Using rule (3) above, the expression is equivalent to: $=\log_3{x} - \left(\log_3{3}+\log_3{3}\right)$ Using rule (3) above, the expression above simplifies to: $=\log_3{x} - (1+1) \\=\log_3{x} - 2$
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