Solve z=3/y^2-1/sqrt[3]{x}+ln5

$$z = \frac { 3 } { y ^ { 2 } } - \frac { 1 } { \sqrt[ 3 ] { x } } + \ln 5$$

Solve for x (complex solution)

$$x=\frac{y^{6}}{\left(-zy^{2}+\ln(5)y^{2}+3\right)^{3}}$$

$$arg(\frac{y^{2}}{-zy^{2}+\ln(5)y^{2}+3})<\frac{2\pi }{3}\text{ and }y\neq 0\text{ and }-zy^{2}+\ln(5)y^{2}+3\neq 0\text{ and }z\neq \ln(5)+\frac{3}{y^{2}}$$

Solve for y (complex solution)

$$y=-\sqrt{3}i\left(-\sqrt[3]{x}z+\ln(5)\sqrt[3]{x}-1\right)^{-\frac{1}{2}}\sqrt[6]{x}$$

$$y=\sqrt{3}i\left(-\sqrt[3]{x}z+\ln(5)\sqrt[3]{x}-1\right)^{-\frac{1}{2}}\sqrt[6]{x}\text{, }x\neq 0\text{ and }z\neq \ln(5)-x^{-\frac{1}{3}}$$

Solve for x

$$x=\frac{y^{6}}{\left(-zy^{2}+\ln(5)y^{2}+3\right)^{3}}$$

$$z\neq \ln(5)+\frac{3}{y^{2}}\text{ and }y\neq 0\text{ and }-zy^{2}+\ln(5)y^{2}+3\neq 0$$

Solve for y

$$y=\sqrt{3}\sqrt[6]{-\frac{x}{\left(-\sqrt[3]{x}z+\ln(5)\sqrt[3]{x}-1\right)^{3}}}$$

$$y=-\sqrt{3}\sqrt[6]{-\frac{x}{\left(-\sqrt[3]{x}z+\ln(5)\sqrt[3]{x}-1\right)^{3}}}\text{, }x\neq 0\text{ and }z\geq \frac{\ln(5)\sqrt[3]{x}-1}{\sqrt[3]{x}}\text{ and }z\neq \ln(5)-\frac{1}{\sqrt[3]{x}}$$