What does $\frac12({\ln b}^2-{\ln a}^2) $ equal to

Question

How can $$\frac12({(\ln b)}^2-({\ln a})^2) $$ be equal to $$\frac12{\ln{(\frac ba)}{\ln (ab)}} $$

I know all the logarithmic properties, but I have no idea where to start

Answer 1

$$\frac12({(\ln b)}^2-({\ln a})^2)=\frac12(\ln b +\ln a)(\ln b -\ln a)=\frac12(\ln (ba))(\ln \frac{b}{a})$$