Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.4 Properties of Logarithmic Functions - 12.4 Exercise Set: 52

Answer

$\log_c \dfrac{p^3\sqrt{t}}{7}$

Work Step by Step

Using the properties of logarithms, the given expression, $ 3\log_c p+\dfrac{1}{2}\log_c t-\log_c 7 ,$ is equivalent to \begin{array}{l}\require{cancel} \log_c p^3+\log_c t^{1/2}-\log_c 7 \\\\= \log_c p^3+\log_c \sqrt{t}-\log_c 7 \\\\= \log_c \left( p^3\sqrt{t} \right)-\log_c 7 \\\\= \log_c \dfrac{p^3\sqrt{t}}{7} .\end{array}
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