Answer
$ a-b$
Work Step by Step
Recall:
$\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$
Using the rule above gives:
$\ln \left(\dfrac{2}{3} \right) = \ln2-\ln3$
With $\ln3 = b \hspace{20pt} \text{and} \hspace{20pt} \ln2=a$, then
$\ln2-\ln3 = a-b$
Therefore
$\ln \left(\dfrac{2}{3} \right) = \boxed{a-b}$
