Algebra 2 Common Core

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

Chapter 7 - Exponential and Logarithmic Functions - Chapter Test - Page 491: 20

Answer

$\log{3}+3\log{x}+2\log{y}$

Work Step by Step

Recall: \begin{align*}n \cdot \log_a{b}&=\log_a{\left(b^n\right)} &\text{( Power Rule)}\\\\ \log_a{b}+\log_a{c}&=\log_a{bc} &\text{(Product Rule)}\\\\ \log_a{b}-\log_a{c}&=\log_a{\frac{b}{c}} &\text{(Quotient Rule)}\end{align*} Use the Product Rule to obtain: \begin{align*} &=\log{3}+\log{x^3}+\log{y^2} \end{align*} Use the Power Rule to obtain: \begin{align*} &=\log{3}+3\log{x}+2\log{y}\\ \end{align*}
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