Given expression $=\log_{xyz}(xy)+\log_{xyz}(yz)+\log_{xyz}(zx)=\log_{xyz}(xy \times yz \times zx)=\log_{xyz}(xyz)^{2}=2\log_{xyz}(xyz)=2\times 1=2$. $[\because \log_{a}x=\frac{1}{\log_{x}a}]$
Explanation as extracted from the printed page; notation may be imperfect.