解決s_{3}^P_{3}=U |Microsoft數學求解器

$$s _ { 3 } ^ { P _ { 3 } } = U$$

解 P_3 (復數求解)

$$\left\{\begin{matrix}P_{3}=\frac{2\pi n_{1}i}{\ln(s_{3})}+\log_{s_{3}}\left(U\right)\text{, }n_{1}\in \mathrm{Z}\text{, }&U\neq 0\text{ and }s_{3}\neq 1\text{ and }s_{3}\neq 0\\P_{3}\in \mathrm{C}\text{, }&\left(s_{3}=0\text{ and }U=0\right)\text{ or }\left(s_{3}=1\text{ and }U=1\right)\end{matrix}\right.$$

解 U (復數求解)

$$U=s_{3}^{P_{3}}$$

解 P_3

$$\left\{\begin{matrix}P_{3}=\log_{s_{3}}\left(U\right)\text{, }&U>0\text{ and }s_{3}\neq 1\text{ and }s_{3}>0\\P_{3}\in \mathrm{R}\text{, }&\left(s_{3}=1\text{ and }U=1\right)\text{ or }\left(s_{3}=-1\text{ and }U=-1\text{ and }Denominator(P_{3})\text{bmod}2=1\text{ and }Numerator(P_{3})\text{bmod}2=1\right)\\P_{3}>0\text{, }&s_{3}=0\text{ and }U=0\end{matrix}\right.$$

解 U

$$U=s_{3}^{P_{3}}$$

$$\left(s_{3}<0\text{ and }Denominator(P_{3})\text{bmod}2=1\right)\text{ or }\left(s_{3}=0\text{ and }P_{3}>0\right)\text{ or }s_{3}>0$$