$$\log_{x^{2}}x\times \log_{y^{2}}y\times \log_{z^{2}}z=\frac{1}{8}$$
$\left\{\begin{matrix}x=-\left(\frac{\ln(y^{2})}{\ln(y)-\ln(2)}\right)^{\frac{4}{3}}\text{, }&y\neq \sqrt[3]{2}\text{ and }y<2\text{ and }y>1\text{ and }z>0\text{ and }z\neq 1\\x=\left(\frac{2\ln(y)}{\ln(y)-\ln(2)}\right)^{\frac{4}{3}}\text{, }&y\neq \frac{1}{2}\text{ and }\left(y>2\text{ or }y<1\right)\text{ and }y>0\text{ and }z>0\text{ and }z\neq 1\end{matrix}\right.$
