## College Algebra (10th Edition)

$-a$
$\bf{\text{Solution Outline:}}$ To write the given expression, $\ln0.5 ,$ 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\dfrac{1}{2} .\end{array} Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent to: \begin{array}{l}\require{cancel} \ln1-\ln2 .\end{array} Since $\ln1=0,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 0-\ln2 \\\\= -\ln2 .\end{array} By substitution, since $a=\ln2,$ the expression above is equivalent to: \begin{array}{l}\require{cancel} -a .\end{array}