## College Algebra (11th Edition)

Published by Pearson

# Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 81

#### Answer

$\log_a [(z+1)^2(3z+2)]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the Laws of Logarithms to write the given expression, $2\log_a (z+1)+\log_a (3z+2) ,$ as a single logarithm. $\bf{\text{Solution Details:}}$ Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_a (z+1)^2+\log_a (3z+2) .\end{array} Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_a [(z+1)^2(3z+2)] .\end{array}

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