Issolvi z^x=1/9

$$z ^ { x } = 1 / 9$$

Solvi għal x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(z)}-2\log_{z}\left(3\right)$$

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

$$z\neq 1\text{ and }z\neq 0$$

Solvi għal z (complex solution)

$$z=e^{-\frac{2\pi n_{1}\left(Im(x)+iRe(x)\right)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}\times 9^{\frac{-Re(x)+iIm(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}}}$$

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

Solvi għal x

$$x=-2\log_{z}\left(3\right)$$

$$z\neq 1\text{ and }z>0$$

Solvi għal z

$$\left\{\begin{matrix}z=-\left(\frac{1}{9}\right)^{\frac{1}{x}}\text{, }&x\neq 0\text{ and }Numerator(x)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\\z=\left(\frac{1}{9}\right)^{\frac{1}{x}}\text{, }&x\neq 0\end{matrix}\right.$$