求解 y^l=e^6x

$$y ^ { l } = e ^ { 6 x }$$

求解 l 的值 (复数求解)

$$\left\{\begin{matrix}l=\frac{2\pi n_{1}i}{\ln(y)}+\frac{6x}{\ln(y)}\text{, }n_{1}\in \mathrm{Z}\text{, }&y\neq 1\text{ and }y\neq 0\\l\in \mathrm{C}\text{, }&y=1\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }x=\frac{\pi n_{2}i}{3}\end{matrix}\right.$$

求解 x 的值 (复数求解)

$$x=\frac{l\ln(y)}{6}+\frac{\pi n_{1}i}{3}$$

$$n_{1}\in \mathrm{Z}$$

$$y\neq 0$$

求解 l 的值

$$\left\{\begin{matrix}l=\frac{6x}{\ln(y)}\text{, }&y\neq 1\text{ and }y>0\\l\in \mathrm{R}\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

求解 x 的值

$$x=\frac{l\ln(y)}{6}$$

$$\left(y<0\text{ and }Denominator(l)\text{bmod}2=1\text{ and }y^{l}>0\right)\text{ or }\left(y>0\text{ and }y^{l}\geq 0\right)$$