Resolver Y=ln(9x^3)

$$Y = \ln ( 9 x ^ { 3 } )$$

Ebatzi: Y (complex solution)

$$Y=\ln(x^{3})+2\ln(3)$$

$$x\neq 0$$

Ebatzi: x (complex solution)

$$x=\frac{\sqrt[3]{3}ie^{\frac{Y}{3}+\frac{\pi i}{6}}}{3}$$

$$x=\frac{\sqrt[3]{3}e^{\frac{Y}{3}}}{3}$$

$$x=-\frac{\sqrt[3]{3}e^{\frac{Y+\pi i}{3}}}{3}\text{, }Im(\ln(e^{Y}))-Im(Y)=0$$

Ebatzi: Y

$$Y=3\ln(x)+2\ln(3)$$

$$x>0$$

Ebatzi: x

$$x=\frac{\sqrt[3]{3}e^{\frac{Y}{3}}}{3}$$