Solve y=sin(logsqrt{x})

$$y = \sin ( \log \sqrt { x } )$$

Solve for x (complex solution)

$$x=10^{\left(-2i\right)\ln(iy+\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+4\pi n_{1}}\text{, }n_{1}\in \mathrm{Z}\text{, }Im(\ln(10^{\left(-i\right)\ln(iy+\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+2\pi n_{1}}))+\ln(10)Re(\ln(iy+\left(1+\left(-1\right)y^{2}\right)^{\frac{1}{2}}))=0$$

$$x=10^{\left(-2i\right)\ln(iy+\left(-1\right)\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+4\pi n_{2}}\text{, }n_{2}\in \mathrm{Z}\text{, }Im(\ln(10^{\left(-i\right)\ln(iy+\left(-1\right)\left(\left(-1\right)y^{2}+1\right)^{\frac{1}{2}})+2\pi n_{2}}))+\ln(10)Re(\ln(iy+\left(-1\right)\left(1+\left(-1\right)y^{2}\right)^{\frac{1}{2}}))=0$$

Solve for y (complex solution)

$$y=\sin(\log(\sqrt{x}))$$

$$x\neq 0$$

Solve for y

$$y=\sin(\frac{\log(x)}{2})$$

$$x>0$$