Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.5 Properties of Logarithms - 5.5 Assess Your Understanding - Page 305: 24



Work Step by Step

We know that $\log_a {b}=\dfrac{\log_c {b}}{\log_c {a}}$. Hence, $\log_3 {8}\cdot \log_8 {9} \\=\dfrac{\log{8}}{\log{3}}\cdot\dfrac{\log{9}}{\log{8}} \\=\dfrac{\log{9}}{\log{3}} \\=\log_3 {9} \\=\log_3 {(3^2)}$ Use the rule $\log_a{a^x}=x$ to obtain: $\log_3{(3^2)}=2$
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