Answer
$a-b$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To write the given expression, $
\ln\dfrac{2}{3}
,$ in terms of $a$ and $b,$ where $a=\ln2$ and $b=\ln3,$ use the laws of logarithms and substitution.
$\bf{\text{Solution Details:}}$
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}
\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}