Answer
$-a$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}