Answer
$b-a$
Work Step by Step
With $1.5=\frac{3}{2}$, then
$\ln(1.5) = \ln \left(\dfrac{3}{2} \right)$
Recall that $\ln\left(\dfrac{M}{N}\right) = \ln M-\ln N$.
Using the rule above gives:
$\ln \left(\dfrac{3}{2} \right) = \ln3-\ln2$
With $\ln3 = b \hspace{20pt} \text{and} \hspace{20pt} \ln2=a$, then
$\ln3-\ln2 = b-a$
Therefore,
$\ln1.5 = \boxed{b-a}$
