Solve 2^x^y^z+54=129

$${ 2 }^{ { x }^{ { y }^{ z } } } +54=129$$

Solve for x (complex solution)

$$x\in \cup n_{2},\ln(2)^{-\frac{Re(y^{z})-iIm(y^{z})}{\left(Re(y^{z})\right)^{2}+\left(Im(y^{z})\right)^{2}}}e^{\frac{\arctan(\frac{2\pi n_{1}}{\ln(75)})Im(y^{z})-\pi sign(n_{1})Im(y^{z})-2\pi n_{2}Im(y^{z})+\pi Im(y^{z})+i\arctan(\frac{2\pi n_{1}}{\ln(75)})Re(y^{z})-\pi isign(n_{1})Re(y^{z})-2\pi n_{2}iRe(y^{z})+\pi iRe(y^{z})}{\left(Re(y^{z})\right)^{2}+\left(Im(y^{z})\right)^{2}}}\left(4\left(\pi n_{1}\right)^{2}+\ln(75)^{2}\right)^{\frac{Re(y^{z})-iIm(y^{z})}{2\left(\left(Re(y^{z})\right)^{2}+\left(Im(y^{z})\right)^{2}\right)}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for y (complex solution)

$$y\in \cup n_{2},\cup n_{3},\left(\frac{|-\ln(\ln(75)+2\pi n_{1}i)-2\pi n_{2}i+\ln(\ln(2))|}{|\ln(x)|}\right)^{\frac{Re(z)-iIm(z)}{\left(Re(z)\right)^{2}+\left(Im(z)\right)^{2}}}e^{\frac{Im(z)arg(\frac{\ln(\ln(75)+2\pi n_{1}i)-\ln(\ln(2))}{\ln(x)}+\frac{2\pi n_{2}i}{\ln(x)})+iRe(z)arg(\frac{\ln(\ln(75)+2\pi n_{1}i)-\ln(\ln(2))}{\ln(x)}+\frac{2\pi n_{2}i}{\ln(x)})}{\left(Re(z)\right)^{2}+\left(Im(z)\right)^{2}}-\frac{2\pi n_{3}iRe(z)}{\left(Re(z)\right)^{2}+\left(Im(z)\right)^{2}}-\frac{2\pi n_{3}Im(z)}{\left(Re(z)\right)^{2}+\left(Im(z)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

$$x\neq 1\text{ and }x\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=\left(\log_{2}\left(75\right)\right)^{\frac{1}{y^{z}}}\text{, }&\left(y<0\text{ and }Denominator(z)\text{bmod}2=1\right)\text{ or }y>0\\x=-\left(\log_{2}\left(75\right)\right)^{\frac{1}{y^{z}}}\text{, }&y\neq 0\text{ and }\left(Denominator(z)\text{bmod}2=1\text{ or }y>0\right)\text{ and }Numerator(y^{z})\text{bmod}2=0\text{ and }Denominator(y^{z})\text{bmod}2=1\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}\text{, }&\left(x>0\text{ and }Numerator(z)\text{bmod}2=1\text{ and }Denominator(z)\text{bmod}2=1\text{ and }\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}\neq 0\text{ and }x<1\right)\text{ or }\left(\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}>0\text{ and }z\neq 0\text{ and }x>1\right)\text{ or }\left(\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}<0\text{ and }z\neq 0\text{ and }Denominator(z)\text{bmod}2=1\text{ and }x>1\right)\\y=-\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}\text{, }&\left(x>0\text{ and }x<1\text{ and }Numerator(z)\text{bmod}2=1\text{ and }Numerator(z)\text{bmod}2=0\text{ and }Denominator(z)\text{bmod}2=1\text{ and }\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}\neq 0\right)\text{ or }\left(x>1\text{ and }z\neq 0\text{ and }\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}<0\text{ and }Numerator(z)\text{bmod}2=0\right)\text{ or }\left(x>1\text{ and }z\neq 0\text{ and }\left(-\frac{\ln(\ln(2))-\ln(\ln(75))}{\ln(x)}\right)^{\frac{1}{z}}>0\text{ and }Numerator(z)\text{bmod}2=0\text{ and }Denominator(z)\text{bmod}2=1\right)\\y\neq 0\text{, }&z=0\text{ and }x=\log_{2}\left(75\right)\end{matrix}\right.$$