## College Algebra (10th Edition)

Published by Pearson

# Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding: 29

#### Answer

$a+b$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To write the given expression, $\ln6 ,$ in terms of $a$ and $b,$ where $a=\ln2$ and $b=\ln3,$ use the laws of logarithms and substitution. $\bf{\text{Solution Details:}}$ The given expression is equivalent to \begin{array}{l}\require{cancel} \ln(2\cdot3) .\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} \ln2+\ln3 .\end{array} By substitution, since $a=\ln2$ and $b=\ln3,$ the expression above is equivalent to \begin{array}{l}\require{cancel} a+b .\end{array}

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