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: 39


3$\log x$ + 4$\log y$ - 6$\log z$

Work Step by Step

$Expand$ $the$ $expression$: $\log \frac{x^3y^4}{z^6}$ Apply the Second Law of Logarithms $\log \frac{x^3y^4}{z^6}$ = $\log {x^3y^4}$ - $\log z^6$ Apply the First Law of Logarithms for $\log {x^3y^4}$ $\log {(x^3\times y^4)}$ = $\log x^3$ + $\log y^4$ $\log x^3$ + $\log y^4$ - $\log z^6$ Apply the Third Law of Logarithms for $\log x^3$, $\log y^4$, and $\log z^6$ $\log x^3$ = 3$\log x$ $\log y^4$ = 4$\log y$ $\log z^6$ = 6$\log z$ Assemble the expression 3$\log x$ + 4$\log y$ - 6$\log z$
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