Issolvi {l}{10^1-x=5}{y=x}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { 10 ^ {1 - x} = 5 }\\ { y = x }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solvi għal x, y, z, a, b, c (complex solution)

$$x=\log(2)+2\pi n_{1}i\log(e)$$

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

$$y=\log(2)+2\pi n_{1}i\log(e)$$

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

$$z\in \cup n_{1},\log(2)+2\pi n_{1}i\log(e)$$

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

$$a\in \cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\log(2)+2\pi n_{1}i\log(e)$$

$$z=\frac{2\pi n_{1}i}{\ln(10)}+\frac{\ln(2)}{\ln(10)}$$

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

$$b\in \cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\log(2)+2\pi n_{1}i\log(e)$$

$$a=\frac{2\pi n_{1}i}{\ln(10)}+\frac{\ln(2)}{\ln(10)}\text{ and }z=\frac{2\pi n_{1}i}{\ln(10)}+\frac{\ln(2)}{\ln(10)}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }z=\log(2)+2\pi n_{1}i\log(e)\right)$$

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

$$c\in \cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\cup n_{1},\log(2)+2\pi n_{1}i\log(e)$$

$$b=\frac{2\pi n_{1}i}{\ln(10)}+\frac{\ln(2)}{\ln(10)}\text{ and }a=\frac{2\pi n_{1}i}{\ln(10)}+\frac{\ln(2)}{\ln(10)}\text{ and }z=\frac{2\pi n_{1}i}{\ln(10)}+\frac{\ln(2)}{\ln(10)}$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }z=\log(2)+2\pi n_{1}i\log(e)\right)$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }z=\log(2)+2\pi n_{1}i\log(e)\right)\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }\left(\exists n_{1}\in \mathrm{Z}\text{ : }a=\log(2)+2\pi n_{1}i\log(e)\text{, }z=\ln(2)\left(\ln(2)+\ln(5)\right)^{-1}+2in_{1}\pi \left(\ln(2)+\ln(5)\right)^{-1}\right)\right)\right)\right)\text{, }n_{1}\in \mathrm{Z}$$

Solvi għal x, y, z, a, b, c

$$c=\log(2)\approx 0.301029996$$