Solucionar y=sin(log_{e}x)

$$y = \sin ( \log _ { e } x )$$

Resolver para x (solución compleja)

$$x=e^{\left(-1\right)\left(i\ln(iy+\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+\left(-2\right)\pi n_{1}\right)}\text{, }n_{1}\in \mathrm{Z}\text{, }Im(\ln(e^{\left(-1\right)\left(i\ln(iy+\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+\left(-2\right)\pi n_{1}\right)}))+Re(\ln(iy+\left(1+\left(-1\right)y^{2}\right)^{\frac{1}{2}}))=0$$

$$x=e^{\left(-1\right)\left(i\ln(iy+\left(-1\right)\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+\left(-2\right)\pi n_{2}\right)}\text{, }n_{2}\in \mathrm{Z}\text{, }Im(\ln(e^{\left(-1\right)\left(i\ln(iy+\left(-1\right)\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+\left(-2\right)\pi n_{2}\right)}))+Re(\ln(iy+\left(-1\right)\left(1+\left(-1\right)y^{2}\right)^{\frac{1}{2}}))=0$$

Resolver para y (solución compleja)

$$y=\sin(\ln(x))$$

$$x\neq 0$$

Resolver para x

$$x=e^{-\arcsin(y)+2\pi n_{1}+\pi }\text{, }n_{1}\in \mathrm{Z}$$

$$x=e^{\arcsin(y)+2\pi n_{2}}\text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq 1$$

Resolver para y

$$y=\sin(\ln(x))$$

$$x>0$$