Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - 7-4 Properties of Logarithms - Practice and Problem-Solving Exercises - Page 466: 18

Answer

$3\log{x} + 5 \log{y}$

Work Step by Step

Use the Product Property of Logarithms. According to this property, $\log_b$ ${mn}$ = $\log_b$ ${m}$ + $\log_b$ ${n}$. Thus, the given expression is equivalent to: $\log$ ${x^3}$ + $\log$ ${y^{5}}$ Use the Power Property of Logarithms to rewrite this expression. The property states that $\log_b$ ${m^n}$ = $n$ $\log_b$ ${m}$. Thus, the expression above is equivalent to: $3$ $\log$ ${x}$ + $5$ $\log$ ${y}$
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