Solve ln(y)=-2/3x^3+6.3

$$\ln ( y ) = \frac{ -2 }{ 3 } { x }^{ 3 } +6.3$$

Solve for x (complex solution)

$$x=\frac{20^{\frac{2}{3}}e^{\frac{i\times 2\pi }{3}}\sqrt[3]{-30\ln(y)+189}}{20}$$

$$x=\frac{20^{\frac{2}{3}}\sqrt[3]{-30\ln(y)+189}}{20}$$

$$x=\frac{20^{\frac{2}{3}}e^{\frac{i\times 4\pi }{3}}\sqrt[3]{-30\ln(y)+189}}{20}\text{, }y\neq 0$$

Solve for y (complex solution)

$$y=e^{-\frac{2x^{3}}{3}+6.3}$$

$$Im(\ln(e^{-\frac{2x^{3}}{3}+\frac{63}{10}}))+\frac{2Im(x^{3})}{3}=0$$

Solve for x

$$x=\frac{20^{\frac{2}{3}}\sqrt[3]{-30\ln(y)+189}}{20}$$

$$y>0$$

Solve for y

$$y=e^{-\frac{2x^{3}}{3}+6.3}$$