Los 2^x+1+z^x-1=20 op

$$2 ^ { x + 1 } + z ^ { x - 1 } = 20$$

Oplossen voor z (complex solution)

$$z=\left(|2\left(10-2^{x}\right)|\right)^{\frac{Re(x)-iIm(x)-1}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-2Re(x)+1}}e^{\frac{Im(x)arg(2\left(10-2^{x}\right))+iRe(x)arg(2\left(10-2^{x}\right))-iarg(2\left(10-2^{x}\right))}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-2Re(x)+1}-\frac{2i\pi n_{1}Re(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-2Re(x)+1}-\frac{2\pi n_{1}Im(x)}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-2Re(x)+1}+\frac{2i\pi n_{1}}{\left(Re(x)\right)^{2}+\left(Im(x)\right)^{2}-2Re(x)+1}}$$

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

Oplossen voor z

$$\left\{\begin{matrix}z=\left(2\left(10-2^{x}\right)\right)^{\frac{1}{x-1}}\text{, }&\left(Numerator(x-1)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>\log_{2}\left(10\right)\right)\text{ or }\left(x\neq 1\text{ and }Numerator(x-1)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x<\log_{2}\left(10\right)\right)\text{ or }\left(\left(20-2\times 2^{x}\right)^{\frac{1}{x-1}}>0\text{ and }x\neq 1\text{ and }x\leq \log_{2}\left(10\right)\right)\text{ or }\left(\left(20-2\times 2^{x}\right)^{\frac{1}{x-1}}<0\text{ and }x\neq 1\text{ and }x\leq \log_{2}\left(10\right)\text{ and }Denominator(x)\text{bmod}2=1\right)\text{ or }x=\log_{2}\left(10\right)\\z=-\left(2\left(10-2^{x}\right)\right)^{\frac{1}{x-1}}\text{, }&\left(x\neq 1\text{ and }\left(20-2\times 2^{x}\right)^{\frac{1}{x-1}}>0\text{ and }Numerator(x-1)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x<\log_{2}\left(10\right)\right)\text{ or }\left(x\neq 1\text{ and }\left(20-2\times 2^{x}\right)^{\frac{1}{x-1}}<0\text{ and }Numerator(x-1)\text{bmod}2=0\text{ and }x<\log_{2}\left(10\right)\right)\text{ or }\left(x=\log_{2}\left(10\right)\text{ and }Numerator(\log_{2}\left(10\right)-1)\text{bmod}2=0\right)\text{ or }\left(x\neq 1\text{ and }Numerator(x-1)\text{bmod}2=0\text{ and }Numerator(x-1)\text{bmod}2=1\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x<\log_{2}\left(10\right)\right)\text{ or }\left(Numerator(x-1)\text{bmod}2=1\text{ and }Numerator(x-1)\text{bmod}2=0\text{ and }Denominator(x)\text{bmod}2=1\text{ and }x>\log_{2}\left(10\right)\right)\end{matrix}\right,$$