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: 37

Answer

$2+\log_5{x}$

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 $25=5(5)$. So the given expression is equivalent to: $\log_5{(5\cdot5\cdot x)}$ Using rule (1) above, the given expression is equivalent to: $=\log_5{5} + \log_5{5} + \log_5{x}$ Using rule (3) above, the expression above simplifies to: $=1+1 + \log_5{x} \\=2+\log_5{x}$
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