College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.4 - Laws of Logarithms - 4.4 Exercises - Page 395: 16



Work Step by Step

RECALL: (1) $\log_b{M}+\log_b{N}=\log_b{MN}$ (2) $\log_b{M}−\log_b{N}=\log_b{\frac{M}{N}}$ (3) $\log_b{(b^x)}=x$ (4) $\log_b{b}=1$ Write $125$ as $5^3$ to obtain: $=\log_5{\left(\frac{1}{\sqrt{5^3}}\right)}$ Use the rule "$\sqrt{a^n}=a^{\frac{n}{2}}$" to obtain: $=\log_5{\left(\dfrac{1}{5^{\frac{3}{2}}}\right)}$ Use the rule "$\dfrac{1}{a^m} = a^{-m}$" to obtain: $=\log_5{(5^{-\frac{3}{2}})}$ Use rule (3) above to obtain: $=-\dfrac{3}{2}$
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