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

Hint: $x^2-y^2=(x+y)(x-y)$ – J. W. Tanner Dec 24 '19 at 17:57 — J. W. Tanner, Dec 24 '19 at 17:57

score 3 · Accepted Answer · answered Dec 24 '19 at 18:05

3

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

answered Dec 24 '19 at 18:05

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1 Answers1