حل =log_{2}z^-x+1/z^x+1=1

$$= \log _ { 2 } \frac { z ^ { - x } + 1 } { z ^ { x } + 1 } = 1$$

حل مسائل x

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

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

حل مسائل z

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