Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.4 - Properties of Logarithms - Exercise Set: 28

Answer

$3\log_b{x}+\log_b{y}-2\log_b{z}$

Work Step by Step

RECALL: (1) $\log{(b^c)}=c \cdot \log{b}$ (2) $\log_b{(xy)} = \log_b{x} + \log_b{y}$ (3) $\log_b{(\frac{x}{y})}=\log_b{x} - \log_b{y}$ Use rule (3) above to obtain: $=\log_b{(x^3y)}-\log_b{(z^2)}$ Use rule (2) above to obtain: $=\log_b{(x^3)} +\log_b{y} - \log_b{(z^2)}$ Use rule (1) above to obtain: $=3\log_b{x}+\log_b{y}-2\log_b{z}$
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