Solve n^P_{7}=13*n-1^P_{6}

$$n ^ { P _ { 7 } } = 13 \cdot n - 1 ^ { P _ { 6 } }$$

Solve for P_6 (complex solution)

$$P_{6}\in \mathrm{C}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }P_{7}=\frac{2\pi n_{1}i}{\ln(n)}+\log_{n}\left(13n-1\right)\text{ and }n\neq \frac{1}{13}\text{ and }n\neq 1\text{ and }n\neq 0$$

Solve for P_7 (complex solution)

$$P_{7}=\frac{2\pi n_{1}i}{\ln(n)}+\log_{n}\left(13n-1\right)$$

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

$$n\neq \frac{1}{13}\text{ and }n\neq 1\text{ and }n\neq 0$$

Solve for P_6

$$P_{6}\in \mathrm{R}$$

$$\left(13n-n^{P_{7}}-1=0\text{ and }n<0\text{ and }Denominator(P_{7})\text{bmod}2=1\right)\text{ or }\left(P_{7}=\log_{n}\left(13n-1\right)\text{ and }n\neq 1\text{ and }n>\frac{1}{13}\right)$$

Solve for P_7

$$P_{7}=\log_{n}\left(13n-1\right)$$

$$n>\frac{1}{13}\text{ and }n\neq 1$$