y=sin(log_{e}sqrt{x}) ઉકેલો

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

x માટે ઉકેલો (જટિલ સમાધાન)

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

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

y માટે ઉકેલો (જટિલ સમાધાન)

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

$$x\neq 0$$

x માટે ઉકેલો

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

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

y માટે ઉકેલો

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

$$x>0$$