Answer
$\displaystyle \ln\frac{x-2}{x+2}$
Work Step by Step
See Th.5.2.
Property $1$ : $\ln(1)=0$
Property $2$ : $\ln(ab)=\ln a + \ln b$
Property $3$ : $\ln(a^{n})=n\cdot\ln a $
Property 4 : $\displaystyle \ln(\frac{a}{b})=\ln a - \ln b$
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$\ln(x-2)-\ln(x+2)$= ... property $4$...$=\displaystyle \ln\frac{x-2}{x+2}$