Leysa (x^7)^5=x^r

$$( x ^ { 7 } ) ^ { 5 } = x ^ { r }$$

Leystu fyrir r (complex solution)

$$\left\{\begin{matrix}r=\frac{2\pi n_{1}i}{\ln(x)}+35\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 0\text{ and }x\neq 1\\r\in \mathrm{C}\text{, }&x=0\text{ or }\left(x=1\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(\exists n_{3}\in \mathrm{Z}\text{ : }n_{2}=35n_{3}\right)\right)\end{matrix}\right.$$

Leystu fyrir r

$$\left\{\begin{matrix}\\r=35\text{, }&\text{unconditionally}\\r\in \mathrm{R}\text{, }&x=1\text{ or }\left(x=-1\text{ and }Denominator(r)\text{bmod}2=1\text{ and }Numerator(r)\text{bmod}2=1\right)\\r>0\text{, }&x=0\end{matrix}\right.$$

Leystu fyrir x

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=-1\text{, }&Denominator(r)\text{bmod}2=1\text{ and }Numerator(r)\text{bmod}2=1\\x=0\text{, }&r>0\\x\neq 0\text{, }&r=35\end{matrix}\right.$$