Solve y=(logy)^a+x^logx

$$y = ( \log y ) ^ { a } + x ^ { \log x }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{\ln(y-x^{\log(x)})}{\ln(\ln(y))-\ln(\ln(10))}+\frac{2i\pi n_{1}}{\ln(\ln(y))-\ln(\ln(10))}\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq x^{\log(x)}\text{ and }x\neq 0\text{ and }y\neq 10\text{ and }y\neq 1\text{ and }y\neq 0\\a\in \mathrm{C}\text{, }&\left(y=1\text{ and }x=1\right)\text{ or }\left(y=1\text{ and }x=-1\text{ and }Numerator(\pi i\log(e))\text{bmod}2=0\right)\text{ or }\left(y=10\text{ and }x^{\log(x)}=9\text{ and }x\neq 0\right)\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\ln(y-x^{\log(x)})}{\ln(\ln(y))-\ln(\ln(10))}\text{, }&x>0\text{ and }y\neq 10\text{ and }y>1\text{ and }y>x^{\log(x)}\\a\in \mathrm{R}\text{, }&\left(y=10\text{ and }x^{\log(x)}=9\text{ and }x>0\right)\text{ or }\left(y=\frac{1}{10}\text{ and }x^{\log(x)}=\frac{11}{10}\text{ and }x>0\text{ and }Denominator(a)\text{bmod}2=1\text{ and }Numerator(a)\text{bmod}2=1\right)\\a>0\text{, }&x=1\text{ and }y=1\end{matrix}\right.$$