How to solve $\log \sqrt[3]{x} = \sqrt{\log x} ?$ How to solve $$\log \sqrt[3]{x} = \sqrt{\log x} $$

Using $$m\log a=\log(a^m)$$ when both logs are defined 
$$\log\sqrt[3] x=\sqrt{\log x}\implies\frac13 \log x=\sqrt{\log x}$$
$$\sqrt{\log x}(\sqrt{\log x}-3)=0$$
$$\sqrt{\log x}=0\iff \log x=0\iff x=1$$
$$\sqrt{\log x}-3=0\iff \log x=9$$
