Решете y=log({left(2x8/x^3xright)}^2)

$$y= \log ( { \left( \frac{ 2x8 }{ { x }^{ 3 } } x \right) }^{ 2 } )$$

Реши за x (complex solution)

$$x=i\sqrt{2x_{8}}\times 10^{-\frac{y}{4}}$$

$$x=\sqrt{2x_{8}}\times 10^{-\frac{y}{4}}$$

$$x=-\sqrt{2x_{8}}\times 10^{-\frac{y}{4}}$$

$$x=-i\sqrt{2x_{8}}\times 10^{-\frac{y}{4}}\text{, }x_{8}\neq 0\text{ and }Im(\ln(5^{y}\times 2^{y-2}))-\ln(2)Im(y)-\ln(5)Im(y)=0$$

Реши за x_8 (complex solution)

$$x_{8}=-\frac{x^{2}\times 10^{\frac{y}{2}}}{2}$$

$$x_{8}=\frac{x^{2}\times 10^{\frac{y}{2}}}{2}\text{, }x\neq 0\text{ and }Im(\ln(5^{y}\times 2^{y-2}))-\ln(2)Im(y)-\ln(5)Im(y)=0$$

Реши за x

$$\left\{\begin{matrix}x=\sqrt{-2x_{8}}\times 10^{-\frac{y}{4}}\text{; }x=-\sqrt{-2x_{8}}\times 10^{-\frac{y}{4}}\text{, }&x_{8}<0\\x=\sqrt{2x_{8}}\times 10^{-\frac{y}{4}}\text{; }x=-\sqrt{2x_{8}}\times 10^{-\frac{y}{4}}\text{, }&x_{8}>0\end{matrix}\right,$$

Реши за x_8

$$x_{8}=\frac{x^{2}\times 10^{\frac{y}{2}}}{2}$$

$$x_{8}=-\frac{x^{2}\times 10^{\frac{y}{2}}}{2}\text{, }x\neq 0$$