# Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding - Page 459: 33

$3a$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To write the given expression, $\ln8 ,$ 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} \ln2^3 .\end{array} Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the expression above is equivalent to: \begin{array}{l}\require{cancel} 3\ln2 .\end{array} By substitution, since $a=\ln2,$ the expression above is equivalent to: \begin{array}{l}\require{cancel} 3a .\end{array}

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