Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.4 - Laws of Logarithms - 4.4 exercises - Page 359: 58


$\log_a (\frac{bd^c}{s^r})$

Work Step by Step

$Combine$ $the$ $expresssion$: $\log_a b$ + $c$$\log_a d$ - $r$$\log_a s$ Apply the Third Law of Logarithms for $c$$\log_a d$ and $r$$\log_a s$ $c$$\log_a d$ = $\log_a d^c$ $r$$\log_a s$ = $\log_a s^r$ $\log_a b$ + $\log_a d^c$ - $\log_a s^r$ Apply the First Law of Logarithms for $\log_a b$ + $\log_a d^c$ $\log_a b$ + $\log_a d^c$ = $\log_a (b\times d^c)$ $\log_a (bd^c)$ - $\log_a s^r$ Apply the Second Law of Logarithms $\log_a (bd^c)$ - $\log_a s^r$ = $\log_a (\frac{bd^c}{s^r})$
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