College Algebra 7th Edition

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

Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check: 53

Answer

$\log_2{\left(\dfrac{(x-y)^{\frac{3}{2}}}{(x^2+y^2)^2}\right)}$

Work Step by Step

RECALL: (1) $n \cdot \log_a{P}=\log_a{(P^n)}$ (2) $\log_a{P} + \log_a{Q}=\log_a{(PQ)}$ (3) $\log_a{P} - \log_a{Q}=\log_a{(\frac{P}{Q})}$ (4) $a^m \cdot a^n=a^{m+n}$ Use rule (1) above to obtain $\frac{3}{2}\log_2{(x-y)}-2\log{(x^2+y^2)}= \log_2{[(x-y)^{\frac{3}{2}}]}-\log_2{[(x^2+y^2)^2])}$ Use rule (3) above to obtain: $\log_2{[(x-y)^{\frac{3}{2}}]}-\log_2{[(x^2+y^2)^2])}=\log_2{\left(\dfrac{(x-y)^{\frac{3}{2}}}{(x^2+y^2)^2}\right)}$
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